From the Editor (in Russian) 2 From the Editor 6 A. G. Yakovlev Interval computations - subject of research and useful tool (in Russian) 10 A. G. Yakovlev Interval computations - subject of research and useful tool 27 J. Herzberger, D. Bethke On two algorithms for bounding the inverses of an interval matrix 44 B. S. Dobronets, V. I. Senashov On interval extension of some classes of functions 54 R. B. Kearfott, Chenyi Hu, Manuel Novoa III A review of preconditioners for the interval Gauss-Seidel method 59 E. A. Musaev Narrowing of intervals by partial derivatives 86 S. P. Shary On compatibility of linear tolerance problem 92 B. V. Paluh, B. V. Vasilyov, V. L. Perov Application of interval mathematics for solving technical diagnostics tasks of non-stop manufacture in chemical industry 99

V. S. Zjuzin Review of the book: H. Bauch, K.-U. Jahn, D. Oelschlaegel, H. Suesse, V. Wiebigke "Interval Mathematics (Theory and Application)" (H. Bauch, K.-U. Jahn, D. Oelschlaegel, H. Suesse, V. Wiebigke Intervallmathematik (Teorie und Anwendungen). - Leipzig, BSB B. G. Teubner Verlagsgesellschaft, 1987, 260 S. (Mathematisch-Naturwissenschaftliche Bibliothek, Band 72)) 105 E. A. Musaev Interval Methods for Numerical Computation West Germany, Oberwolfach, 3 - 10. 3 1990 (Information on international meeting) 108 S. P. Shary 7-th All-Union Workshop in Interval Mathematics (Information) 111 Requirements for manuscript preparation (in Russian) 113 Requirements for manuscript preparation 114 Contents 115

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From the Editor 2 From the Editor (in Russian) 4

S. Shary Optimal solution of interval linear algebraic systems. I 7 V. Kreinovich, A. Bernat, E. Villa, Y. Mariscal Parallel Computers. Estimate errors caused by imprecise data 31

R. Hammer, M. Neaga, D. Ratz, D. Shiryaev PASCAL-XSC: A new language for scientific computing 47

The full translation into Russian of ANSI/IEEE standards on computer arithmetic 82 Program package ASIAS 83 Program package ASIAS (in Russian) 84

P. S. Pankov Review of the new monograph: Dobronets B. S., Shaydurov V. V. Two-sided numerical methods 85

Actual problems of applied mathematics. All-Union conference. Saratov, May 20-22, 1991. A brief report (A. V. Zakharov) 87 Actual problems of applied mathematics. All-Union conference. Saratov, May 20-22, 1991. A brief report (A. V. Zakharov, in Russian) 91 A. Davidenkoff Advanced seminar on programming languages for scientific/engineering computation, Leningrad, June 3-6, 1991. A summarizing report 96 Interval subject on the SCAN-1991 symposium. Information (J. Herzberger) 107 Resolution of 8th All-Union Workshop on interval mathematics. Bishkek, October 1-3, 1991 108 Preliminary announcement, call for papers and further information for a conference on numerical analysis with automatic result verification. Lafayette, Louisiana, February 25 - March 1, 1993 110

Bibliography of Soviet works on interval computations. Part 1 115 REQUIREMENTS FOR MANUSCRIPT PREPARATION 123 REQUIREMENTS FOR MANUSCRIPT PREPARATION (in Russian) 125 ADDRESSES OF EDITORIAL BOARD MEMBERS 127 CONTENTS 132

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From the Editor 2 From the Editor (in Russian) 4

B. S. Dobronets On some two-sided methods for solving systems of ordinary differential equations 6 S. M. Rump Inclusion of the solution for large linear systems with M-matrix 22

A. I. Orlov Interval statistics 44

E. A. Musaev Wave computations. A technique for optimal quasi-concurrent self-validation 53 A. G. Yakovlev Classification approach to programming of localizational (interval) computations 61

G. D. Pankova Programming support and algorithmic language for validating computations on ES (IBM 360/370) series computer 86

A review of the book: A. Neumaier, Interval Methods for Systems of Equations (G. Alefeld) 96 List of abstracts from Referativnyi Zhurnal "Matematika" for 1991 98

Interval Mathematics and Its Applications. Workshop 100

Bibliography of Soviet works on interval computations. Part II 104 Requirements for manuscript preparation 112 Requirements for manuscript preparation (in Russian) 114 Addresses of editorial board members 116 Contents 119

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From the Editor 2 From the Editor (in Russian) 4

A. F. Filippov Ellipsoidal estimates for a solution of a system of differential equations 6 S. P. Shary A new class of algorithms for optimal solution of interval linear systems 18 P. S. Pankov Proof of finite-dimensional inequalities by means of interval analysis 30 V. S. Zyuzin On metrization of interval sets I(R), I(R^n) 39Applications and studies of related disciplines

V. Kreinivich, A. Bernat, O. Kosheleva, A. Finkelstein Interval estimates for closure-phase and closure-amplitude in radio astronomy 51

A. Davidenkoff ACRITH-XSC: A programming language for scientific/engineering computation 72

G. G. Menshikov The teaching experience of interval computations at the Department of applied mathematics and control processes of St. -Petersburg University 83

International conference "INTERVAL-92" 86 Mathematical modelling and scientific computation. International conference. Sozopol, Bulgaria, September 14-17, 1993 99

List of abstracts from Referativnyi Zhurnal "Matematika" for 1991 105

Bibliography of Soviet works on interval computations. Part III 107 Requirements for manuscript preparation 116 Requirements for manuscript preparation (in Russian) 118 Addresses of editorial board members 120 Contents 123

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From the editor 2 From the editor (in Russian) 4 From the invited editor 6 From the invited editor (in Russian) 7 A. Akunova, T. A. Akunov and A. V. Ushakov Construction of a comparison system for multivariate control processes with interval state matrix 8 A. B. Babichev, O. B. Kadyrova, T. P. Kashevarova, A. L. Semenov UniCalc as a tool for solving problems with inaccurate and sub-definite data 13 F. Blomquist Interval inclusions for Dawson's integral 17 A. F. Bochkov and L. A. Yakovleva Algorithm for experimental zero-order optimization for plant with bounded amplitude errors 27 A. F. Bochkov and N. V. Zung Identification of nonlinear dynamic objects using interval experimental data 31 D. M. Claudio, M. H. Escardo, and B. R. T. Franciosi An order-theoretical approach to interval analysis 38 A. I. Demchenko, B. V. Peltsverger, O. V. Khavronin Syntesis of transport networks structures under conditions of uncertain initial information 46 B. S. Dobronets Interval methods based on a posteriori estimates 50 I. V. Dugarova An algorithm of interval matrix asymptotic stability testing 56 O. B. Ermakov Two-sided method for solving system of ordinary differential equations with automatic determination of guaranteed estimates 63 T. V. Evtushenko Optimization problems for static plants under uncertainty conditions 70 A. F. Filippov Ellipsoidal error estimates for Adams method 75 N. M. Glazunov On interval extensions of computer algebra systems 80 T. Henriksen and K. Madsen Parallel algorithms for global optimization 88 B. Kearfott, M. Dawande, K. Du and C. Hu INTLIB: A portable Fortran-77 elementary function library 96 N. A. Khlebalin Interval automatic systems - theory, computer-aided design and applications 106 A. V. Korlyukov A new application of interval mathematics 116 International conference on interval and computer-algebraic methods in science and engineering (INTERVAL'94) 122 Contents 126

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V. N. Krishchuk, N. M. Vasilega and G. L. Kozina Interval operations and functions library for FORTRAN 77 programming system and its practice using 2 V. G. Krymsky Algorithmic aims of reliability provision for large-scale dynamic systems with interval parameters 9 G. L. Litvinov Error auto-correction in rational approximation 14 S. M. Markov On the presentation of ranges of monotone functions using interval arithmetic 19 G. G. Menshikov Interval co-integration of differential equations connected by a substitution of the variable 32 E. A. Musaev An approach to reliable computations with THE minimal representation 37 A. S. Narin'yani Ne-factors and natural pragmatics: what do the intervals represent 42 V. M. Nesterov Estimating a range of values of functions using extended interval arithmetics 48 P. S. Pankov and B. D. Bayachorova Using interval methods in cluster analysis and verified representation of connected sets 54 P. S. Senio and P. S. Vengersky Solving systems of special form nonlinear equations by means of some modifications of Runge type interval iterative method 59 S. P. Shary On controlled solution set of interval algebraic systems 66 D. Shiriaev PASCAL-XSC. A portable programming system for scientific computations 76 S. J. Simoff Interval approximate reasoning for expert systems 83 N. V. Skybytsky and T. Yuping Control of the linear dynamic plant with intervally given parameters from the guarantee condition of the required accuracy of the solution 88 E. M. Smagina General problem of the asymptotic steady-output tracking for plant with interval parameters 94 I. G. Ten Synthesis of optimal control under interval uncertainty in models 100 A. P. Voshchinin Some questions of application of interval mathematics in parameter estimation and decision making 107 J. Wolff von Gudenberg Programming language support for scientific computation 116 V. S. Zyuzin The extension of the Frechet derivative concept in the interval-segment analysis 127 Contents 133

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From the Editor 2 From the Editor (in Russian) 4

Vladik Kreinovich, Anatoly V. Lakeyev and Sergey I. Noskov Optimal solution of interval linear systems is intractable (NP-hard) 6 R. Baker Kearfott and Xiaofa Shi A preconditioner selection heuristic for efficient iteration with decomposition of arithmetic expressions for nonlinear algebraic aystems 15 Ljiljana D. Petkovic and Miroslav Trajkovic On some optimal inclusion approximations by discs 34 V. A. Perepelitsa and G. L. Kozina Interval discrete models and multiobjectivity complexity estimates 51 Yilmaz Akyildiz and Mohammad I. Al-Suwaiyel No Pathologies for interval Newton's method 60

International conference "INTERVAL'94" 73

N. A. Khlebalin Review of the Book 79 N. A. Khlebalin Review of the Book (in Russian) 84

Mathematical modelling and scientific computation. International conference. Sozopol, Bulgaria, September 14-17, 1993 99

List of abstracts from Referativnyi Zhurnal "Matematika" for 1991 105

Bibliography of Soviet works on interval computations. Part III 107 Requirements for manuscript preparation 116 Requirements for manuscript preparation (in Russian) 118 Addresses of editorial board members 120 Contents 123

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(Special Issue: Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification. Lafayette, Louisiana, USA, Feb. 25 - March 1, 1993. - Vol. 1)

From the Editor 2 From the Editor (in Russian) 3 Foreword by Prof. R. B. Kearfott 4 Fernando L. Alvarado and Zian Wang Direct Sparse Interval Hull Computations for Thin Non-M-Matrices 5 A. B. Babichev, O. B. Kadyrova, T. P. Kashevarova, A. S. Leshchenko, and A. L. Semenov UniCalc, a Novel Approach to Solving Systems of Algebraic Equations 29 Daniel Berleant Automatically Verified Reasoning with Both Intervals and Probability Density Functions 48 Ole Caprani, Brian Godthaab, and Kaj Madsen Use of a Real-Valued Local Minimum in Parallel Interval Global Optimization 71 Iliano Cervesato, Angelo Montanari, Alessandro Provetti On the Non-monotonic Behaviour of Event Calculus for Deriving Maximal Time Intervals 83 Amanda E. Connell and Robert M. Corless An Experimental Interval Arithmetic Package in Maple 120 Jeffrey S. Ely The VPI Software Package for Variable Precision Interval Arithmetic 135 J. Garloff The Bernstein Algorithm 154 Gregory D. Hager Solving Large Systems of Nonlinear Constraints with Application to Data Modeling 169

Applications of Interval Computations: International Workshop 201 Requirements for manuscript preparation 205 Requirements for manuscript preparation (in Russian) 206 Addresses of the editorial board members 207 Contents 209

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(Special Issue: Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification. Lafayette, Louisiana, USA, Feb. 25 - March 1, 1993. - Vol. 2)

E. R. Hansen Computing Zeros of Functions Using Generalized Interval Arithmetic 3 C. Hu, R. B. Kearfott, and A. Awad On Bounding the Range of Some Elementary Functions in FORTRAN-77 29 R. Van Iwaarden Automatic Differentiation Applied to Unconstrained Nonlinear Optimization with Result Verification 41 L. Jaulin and E. Walter Guaranteed Nonlinear Parameter Estimation via Interval Computations 61 J. B. Keiper Interval Arithmetic in Mathematica 76 L. J. Kohout and I. Stabile Interval-Valued Inference in Medical Knowledge-Based System CLINAID 88 C. Falco Korn and Ch. Ullrich Verified Solution of Linear Systems Based on Common Software Libraries 116 B. P. Kristinsdottir, Z. B. Zabinsky, T. Csendes, and M. E. Tuttle Methodologies for Tolerance Intervals 133 A. Leclerc Parallel Interval Global Optimization and Its Implementation in C++ 148 S. M. Markov Some Interpolation Problems Involving Interval Data 164 M. Nakamura, R. Mines, and V. Kreinovich Guaranteed Intervals for Kolmogorov's Theorem (and Their Possible Relation to Neural Networks) 183

Journal of Symbolic Computations: Special Issue on Validated Numerical Methods and Computer Algebra 200 Requirements for manuscript preparation 202 Requirements for manuscript preparation (in Russian) 203 Addresses of the editorial board members 204 Contents 206

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(Special Issue: Proceedings of the International Conference on Numerical Analysis with Automatic Result Verification. Lafayette, Louisiana, USA, Feb. 25 - March 1, 1993. - Vol. 3)

V. M. Nesterov How To Use Monotonicity-Type Information To Get Better Estimates of the Range of Real-Valued Functions 3 J. Rohn Cheap and Tight Bounds: The Recent Result by E. Hansen Can Be Made More Efficient 13 M. J. Schaefer Precise Zeros of Analytic Functions Using Interval Arithmetic 22 C. A. Schnepper and M. A. Stadtherr Application of a Parallel Interval Newton/Generalized Bisection Algorithm to Equation-Based Chemical Process Flowsheeting 40 M. J. Schulte and E. E. Swartzlander, Jr. Parallel Hardware Designs for Correctly Rounded Elementary Functions 65 L. Simcik and P. Linz Boundary-Based Interval Newton's Method 89 O. Sirisaengtaksin and V. Kreinovich Neural Networks That Are Not Sensitive To The Imprecision of Hardware Neurons 100 U. Storck Verified Calculation of the Nodes and Weights for Gaussian Quadrature Formulas 114 I. B. Turksen Interval Valued Fuzzy Sets and Fuzzy Connectives 125 V. M. Veliov Computation of Integrals of Uncertain Vector Functions 143 E. Villa, A. Bernat, and V. Kreinovich Estimating Errors of Indirect Measurement on Realistic Parallel Machines: Routings on 2-D and 3-D Meshes That are Nearly Optimal 154 K. Villaverde and V. Kreinovich A Linear-Time Algorithm That Locates Local Extrema of a Function of One Variable From Interval Measurement Results 176 A. G. Yakovlev Multiaspectness and Localization 195

J. Wolff von Gudenberg International Conference INTERVAL'94 210 Advertisement 212 Requirements for manuscript preparation 214 Requirements for manuscript preparation (in Russian) 215 Addresses of the editorial board members 216 Contents 218

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From the Editor 2 From the Editor (in Russian) 3

G. Alefeld and G. Mayer A Computer Aided Existence and Uniqueness Proof for an Inverse Matrix Eigenvalue Problem 4 W. J. Luther and W. Otten Verified Inclusion for Eigenvalues of Hill's Equation 28 G. L. Kozina and V. A. Perepelitsa Interval Spanning Trees Problem: Solvability and Computational Complexity 42 H. Schwandt Suboptimal Enclosures for the Interval Buneman Algorithm for Arbitrary Block Dimension 51 O. B. Ermakov Solving Systems of Ordinary Differential Equations Using Adams' Interpolation Method with Guaranteed Accuracy 90

G. G. Menshikov On Different Definitions of Interval Extension: Problems of Teaching 96 Amendment 99

Bibliography of Soviet Works on Interval Computations. Part V 100 Requirements for manuscript preparation 110 Requirements for manuscript preparation (in Russian) 111 Addresses of the editorial board members 112 Contents 114

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From the Editor 2 From the Editor (in Russian) 4

S. P. Shary Solving the Tolerance Problem for Interval Linear Systems 6 N. S. Dimitrova and S. M. Markov On Validated Newton Type Method for Nonlinear Equations 27 V. A. Podchukayev and I. M. Svetlov An Analytical Method of Constructing Hurwitz Interval Polynomials 52

M. Berz and G. Hoffstaetter Exact Bounds on the Long Term Stability of Weakly Nonlinear Systems Applied to the Design of Large Storage Rings 68 V. Kreinovich, T. Swenson, and A. Elentukh Interval Approach to Testing Software 90

1st All-Russian Conference on Countinuous Logic and Its Applications 110 1st All-Russian Conference on Countinuous Logic and Its Applications (in Russian) 110

Bibliography of Soviet Works on Interval Computations. Part VI 116 Requirements for manuscript preparation 127 Requirements for manuscript preparation (in Russian) 128 Addresses of the editorial board members 129 Contents 131

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Foreword by the Invited Editors of the Special Issue 2 Foreword by the Invited Editors of the Special Issue (in Russian) 4 V. Kreinovich and A. Bernat Parallel Algorithms for Interval Computations: An Introduction 6 E. Lyager Finding Local Extremal Points by Using Parallel Interval Methods 63 K. Madsen and O. Toft A Parallel Method for Linear Interval Equations 81 M. Plum Enclosures for Solutions of Parameter-Dependent Nonlinear Elliptic Boundary Value Problems: Theory and Implementation on a Parallel Computer 106 Requirements for manuscript preparation 122 Requirements for manuscript preparation (in Russian) 123 Addresses of the editorial board members 124 Contents 126

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Foreword by Prof. H. Stetter 2 Foreword by Prof. H. Stetter (in Russian) 3 S. Christiansen Interval Methods and Condition Numbers of Linear Algebraic Systems 4 M. Daumas and D. W. Matula Rounding of Floating Point Intervals 28 M. Daumas, Ch. Mazenc, and J.-M. Muller Towards a User Transparent Interval Arithmetic 46 M. T. Nakao Numerical Verifications of Solutions for Nonlinear Hyperbolic Equations 64 W. Luther and W. Otten Computation of Standard Interval Functions in Multiple-Precision Interval Arithmetic 78 E. D. Popova Extended Interval Arithmetic in IEEE Floating-Point Environment 100 Addresses of the editorial board members 130 Contents 132

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Bibliography of Works on Interval Computations Published in Russian B. S. Dobronets, R. B. Kearfott, L. V. Kupriyanova, A. G. Yakovlev, and V. S. Zuizin,

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Preface 3 Preface (in Russian) 5

Formulas for the width of interval products Helmut Ratschek and Jon G.~Rokne 9 Inner estimation of the united solution set of interval linear algebraic system Ludmila Kupriyanova 15 Why intervals? A simple limit theorem that is similar to limit theorems from statistics Vladik Kreinovich 33 A combined method for enclosing all solutions of nonlinear systems of polynomial equations Christine J\"ager and Dietmar Ratz 41

An informal introduction to a high level language with applications to interval mathematics Daniel E. Cooke 65 A parallel interval method implementation for global optimization using dynamic load balancing Jerry Eriksson and Per Lindstr\"om 77

Interval sessions at NAFIPS/IFIS/NASA'94 Vladik Kreinovich and Hung T.~Nguyen 93 Addresses of the Editorial Board Members 99 Information for Authors 101 Contents 103

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Preface (in Russian) 107 From the Editor 108 Parallel interval-based reasoning in medical knowledge-based system CLINAID Ladislav J. Kohout, Isabel Stabile, Hasan Kalantar, Maria F. San-Andres, and John Anderson 109 Applications of interval computations to earthquake-resistant engineering: How to compute derivatives of interval functions fast Vladik Kreinovich, David Nemir, and Efren Gutierrez 141 A reliable linear algebra library for transputer networks Christian P. Ullrich and Roman Reith 173 Parallel accurate linear algebra subroutines Juergen Wolff von Gudenberg 189 Addresses of the Editorial Board Members 201 Information for Authors 203 Contents 205

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Editors' Introduction 209

Application of interval Newton's method to chemical engineering problems Gopalan V. Balaji and J. D. Seader 215 Ockham's razor in interval identification Bo H. Friesen and Vladik Kreinovich 225 An automatic and guaranteed determination of the number of roots of an analytic function interior to a simple closed curve in the complex plane Jonathan Herlocker and Jeffrey Ely 239 A general iterative sparse linear solver and its parallelization for interval Newton methods Chenyi Hu, Anna Frolov, R. Baker Kearfott, and Qing Yang 251 Optimizing INTBIS on the CRAY Y-MP Chenyi Hu, Joe Sheldon, R. Baker Kearfott, and Qing Yang 265 Study on sampling techniques with CMMs Thomas J. McLean and David H. Xu 275 A new characterization of the set of all intervals, based on the necessity to check consistency easily Driss Misane and Vladik Kreinovich 285 Interpolation that leads to the narrowest intervals and its application to expert systems and intelligent control Hung T. Nguyen, Vladik Kreinovich, Bob Lea, and Dana Tolbert 299 A parallel complex zero finder Mark J. Schaefer and Tilmann Bubeck 317 A software interface and hardware design for variable-precision interval arithmetic Michael J. Schulte and Earl E. Swartzlander, Jr. 325 A bright side of NP-hardness of interval computations: interval heuristics applied to NP-problems Bonnie Traylor and Vladik Kreinovich 343

Special Issue 361 1994 Lotfi A. Zadeh Best Paper Award in the field of fuzzy logic 362 Addresses of the Editorial Board Members 363 Information for Authors 365 Contents 367

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Preface 371

Matrix computation of subresultant polynomial remainder sequences in integral domains Alkiviadis G. Akritas, Evgenia K. Akritas, and Genadii I. Malaschonok 375 Numerical methods using defects Boris S. Dobronets 383 An estimate of the absolute value and width of the solution of a linear system of equations with tridiagonal interval matrix by the interval sweep method A. N. Ostylovsky 393 Verification methods for inclusion disks Ljiljana D. Petkovic and Miroslav Trajkovic 403 Design of a parallel linear algebra library for verified computation J. Wolff von Gudenberg 411 Computation of the stability radius of a Schur polynomial: an orthogonal projection approach Q.-H. Wu and M. Mansour 421

International conference on interval methods and computer aided proofs in science and engineering INTERVAL'96 431 II Workshop on Interval Arithmetic 433 IMACS-GAMM International Symposium on Numerical Methods and Error Bounds S. Shary 434 Addresses of the Editorial Board Members 436 Information for Authors 438 Amendments 439 Contents 440

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Algebraic approach to the interval linear static identification, tolerance, and control problems, or One more application of Kaucher arithmetic Sergey P. Shary 3 Bounds of high quality for first kind Volterra integral equations Hans-Juergen Dobner 35 Variable-precision, interval arithmetic coprocessors Michael J. Schulte and Earl E. Swartzlander, Jr. 47

Maximum entropy and interval computations (September notes on summer impressions) Vladik Kreinovich 63

Best student paper award Vladik Kreinovich and Guenter Mayer 81 Call for Papers: Student Issues of Reliable Computing 81 Call for Papers: Special Issue of Reliable Computing on Applications to Geosciences 82

SCAN'95: International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics Andreas Frommer 84 SONIC'95: Student Mini-Symposium on Interval Computations Vladik Kreinovich 86 Interval talks at the first El Paso Shell Oil Symposium Vladik Kreinovich 88 Addresses of the Editorial Board members 89 Information for authors 91 Contents 92

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Preface 95 Mechanising the theory of intervals using OBJ3 Marcilia A. Campos, Augusto C. A. Sampaio, and Alexandre H. F. Brainer 97 Errors in vector processing and the library libavi.a Tiaraju A. Diverio, Ursula A. Fernandes, and Dalcidio M. Claudio 103 Chebyshev acceleration techniques for large complex non Hermitian eigenvalue problems Vincent Heuveline and Miloud Sadkane 111 Interval methods that are guaranteed to underestimate (and the resulting new justification of Kaucher arithmetic) Vladik Kreinovich, Vyacheslav M. Nesterov, and Nina A. Zheludeva 119 On the computational complexity of the solution of linear systems with moduli Anatoly V. Lakeyev 125 Software for high radix on-line arithmetic Thomas Lynch and Michael J. Schulte 133 Self-correcting polynomial programs Guevara Noubir and Henri J. Nussbaumer 139 Reducing division latency with reciprocal caches Stuart F. Oberman and Michael J. Flynn 147 Interval approach challenges Monte Carlo simulation Janne Pesonen and Eero Hyvonen 155 Interval operations involving NaNs Evgenija D. Popova 161 Enclosing solutions of overdetermined systems of linear interval equations Jiri Rohn 167 Numerical solutions of Burgers' equation with a large Reynolds number Masaaki Sugihara and Seiji Fujino 173 Rank of convex combinations of matrices Tomasz Szulc 181 Locating, characterizing and computing the stationary points of a function Michael N. Vrahatis and Evangelia C. Triantafyllou 187

Applications of Reliable Scientific Computing 195

Addresses of the Editorial Board members 204 Information for authors 206 Contents 207

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Preface 211 Robust algorithms that locate local extrema of a function of one variable from interval measurement results: A remark Christoph Eick and Karen Villaverde 213 Fast error estimates for indirect measurements: applications to pavement engineering Carlos Ferregut, Soheil Nazarian, Krishnamohan Vennalaganti, Ching-Chuan Chang, and Vladik Kreinovich 219 Newton's constant of gravitation and verified numerical quadrature Oliver Holzmann, Bruno Lang, and Holger Sch\"utt 229 Two adaptive Gauss-Legendre type algorithms for the verified computation of definite integrals Walter Kr\"amer and Stefan Wedner 241 A quadratic-time algorithm for smoothing interval functions Vladik Kreinovich and Karen Villaverde 255 Optimal interval enclosures for fractionally-linear functions, and their application to intelligent control Robert N. Lea, Vladik Kreinovich, Raul Trejo 265 If we measure a number, we get an interval. What if we measure a function or an operator? Joe Lorkowski and Vladik Kreinovich 287 New slope methods for sharper interval functions and a note on Fischer's acceleration method Jo\~ao B. Oliveira 299 Ordering events: Intervals are sufficient, more general sets are usually not necessary Alessandro Provetti 321

Applications of Reliable Scientific Computing 329 Addresses of the Editorial Board members 332 Information for authors 334 Contents 335

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Preface 339 Mathematical research Linear interval equations: Computing enclosures with bounded relative or absolute overestimation is NP-hard Vladik Kreinovich and Anatoly V. Lakeyev 341 On the speed of convergence of the total step iterative method for a class of interval linear algebraic systems Marina A. Lyashko 351 Improving the efficiency index in enclosing a root of an equation Yixun Shi 357

Some examples using the interval data type in the relational database model John W. Starner 373

Paul Erdos, 1913-1996 383

Double bubble minimizes: Interval computations help in solving a long-standing geometric problem Vladik Kreinovich 387

Reliable Computing in 1997 389 Peter Fishburn receives von Neumann prize 390 Best student paper award Vladik Kreinovich and Guenter Mayer 390

WAI'96: II Workshop on Computer Arithmetic, Interval and Symbolic Computations Marcilia A. Campos 391 Interval'96: International Conference on Interval Methods and Computer Aided Proofs in Science and Engineering J. Wolff von Gudenberg 392 Interval Talks at FUZZ-IEEE'96 Erich Peter Klement and Vladik Kreinovich 394 Addresses of the Editorial Board members 402 Information for authors 404 Contents 405

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Interval'96: International Conference on Interval Methods and Computer-Aided Proofs in Science and Engineering Sep 30 - oct 2, 1996, Wuerzburg, Germany Extended Abstracts Preface

A "Metric" Topology Compatible with Inclusion Monotonicity on Interval Space B. M. Acioly and B. R. Bedregal 7 Robust Stability Investigation Using Frequency Domain Technique F. Akmedjanov and S. Chelyshev 9 On the Evaluation of Functional Ranges Using a Random Interval Arithmetic R. Alt and J.-L. Lamotte 11 A Simplex-like Algorithm for Interval Linear Systems O. Beaumont 13 An Information System Approach to Interval Mathematics B. R. Bedregal and B. M. Acioly 15 Interval Deductions in Continuous Domain Logic B. R. Bedregal and B. M. Acioly 17 A Numerically Rigorous Proof of Curve Veering for a Plate H. Behnke 19 A Fixpoint Approximate Semantics for Cooperating Numerical Solvers F. Benhamou and L. Granvilliers 20 A Library for Real Numbers using Cauchy's Embedded Interval Sequences D. Berthelot and M. Daumas 23 Fast Algorithms for the Evaluation of Partial Derivates and their Application to Interval Slopes C. Bliek 25 Variable Precision in Interval Computations C. Bliek 27 Verified Calculation of the Approximation Error Using Rational Approximation Functions F. Blomquist 29 Existence Test for Asynchronous Interval Iteration O. Caprani, K. Madsen, and O.Stauning 30 Role of Constraints in the Validated Solution of DAEs G. F. Corliss and W. Lodwick 32 Interval Optimization Methods for Process Network Synthesis T. Csendes 33 Symbolic versus Floationg-point Detection of Multivariate Pole Sets A. Cuyt 34 Environment for the Hybrid Numeric Computation A. Cuyt, Y. Godts, and B. Verdonk 35 Computer Assisted Proofs and Scientific Computing H.-J. Dobner 36 Two-sided Multigrid Method for Elliptic Boundary Value Problems B. S. Dobronets 37 A Guaranteed Inclusion of Fixed Point of Difference Operator on a Set of Interval Function with Hausdorff Metric O. B. Ermakov 39 Computer Assisted Proof of Chaos for Lorenz System. Part II. Numerical Algorithms Z. Galias and P. Zgliczynski 40 Bounds for the Range of a Multivariate Polynomial over a Simplex J. Garloff and R. Hungerbuehler 42 Robust Stability Analysis of Polynomials with Polynomial Parameter Dependency J. Garloff and M. Zettler 43 Direct Computation of All Singular Points of Chemical Engineering Models Using Interval Methods V. Gehrke and W. Marquardt 45 Interval Construction within Partially Ordered Object Versions G. Heidenreich, M. Minas, and J. Landauer 47 Proving the Existence of Equilibrum Positions of Particle Systems G. Heindl 49 Helios: A Modeling Language for Global Optimization using Interval Analysis P. Van Hentenryck and L. Michel 50 High Accuracy and High Performance Environment C. A. Hoelbig, R. L. Sagula, U. A. Fernandes, T. A. Diverio, and D. M. Claudio 51 A Computer Oriented Approach to Get Sharp Reliable Error Bounds W. Hofschuster and W. Kraemer 53 Hierarchical Constraint Propagation based on Interval Arithmetic E. Huellermeier 54 Interval Constraint Satisfaction - A New Computational Basis for Spreadsheet Computations E. Hyvoenen and S. De Pascale 56 Finding Global Minima of Maximum Functions by Using Exclusion Functions without Derivatives F. Kalovics and G. Meszaros 57 Some Issues Concerning Convergence of the Method of Subdefinite Computations T. P. Kashevarova and A. L. Semenov 59 A Case Study for the Use of Verifying BLAS in an LAPACK like Verifying Driver-Routine for the Solution of Linear Systems T. Kersten 60 Investigations of Robustness of Modern Structures for Controlled Devices of Cutting Machines of Electric Drives N. A. Khlebalin and A. V. Lazarev 61 Application of a Parallel Verified Block LU-Algorithm to Process Simulation W. Klein 62 Verified Modelling on Circuit Simulation W. Klein 63 On Interval-valued Hermite Splines V. V. Kobkov 64 On the Interval Problems on Graphs G. L. Kozina and V. A. Perepelitsa 65 The Analysis of Complex Dynamic Systems with Interval Models: Decomposition-Based Technique V. Krymsky and A. Yunusov 67 Diagrammatic Representation of Interval Space in Proving Theorems about Interval Relations Z. Kulpa 69 Robust Observer for Linear Dynamic Objects in the Class of Ellipsoidal Sets N. N. Kussul 71 Each Vertex of the Set of Solutions of a Strongly Regular Interval System of Linear Equations is Polynomially Computable A. V. Lakeyev 73 Matrix Games with Interval Parameters V. I. Levin 75 Interval Computations and the Effect of Error Auto-Correction G. L. Litvinov 76 Idempotent Mathematics and Scientific Calculations G. L. Litvinov, V. P. Maslov, and A. Y. Rodionov 77 Approximation Error and Error Accumulation for the Landen Transformation W. Luther and W. Otten 79 On the Algebra of Intervals S. Markov 81 Interval Arithmetic in a Verification Condition Generator W. D. Maurer 82 On Expanding Iterations G. G. Men'shikov 84 Set of Feasible Coefficients for Systems of Linear Interval Equations F. Mraz 86 Topological Methods in Computer Assisted Proofs in Dynamics M. Mrozek 87 A Computational Approach for the Estimates of Constants Related to the Numerical Verification Method for Boundary Value Problems M. T. Nakao 88 Interval and Twin Arithmetics V. Nesterov 89 A Relation Between Morphological and Interval Operations A. T. Popov and S. M. Markov 91 Distributivity of the Directed Intervals and its Computer Algebra Applications E. D. Popova 93 On Optimal Interval Bounds for Reachable Set of Dynamic Systems A. Rogalev 94 Complexity of Some Linear Problems with Interval Data J. Rohn 96 Concurrent Cooperating Solvers over the Reals M. Rueher and C. Solnon 97 Intervals as Real Numbers Specification R. Santiago and B. M. Acioly 99 Production Planning Using Uncertain Data R. Schmieder, J. Schulze, and S. Kutscher 101 Algebraic Approach in the "Outer Problem" for Interval Linear Equations S. P. Shary 102 Fast and Accurate Higher-Order Derivatives of Vector Functions Represented by Fortran 90/77 or C/C++ Codes D. Shiriaev 104 A New Approach to the Modal Regulator Synthesis for Interval Plants with Scalar Input Ye. H. Smagina 105 Interval Mathematical Model and Solution Method of The Rectangles Placement Problem Yu. G. Stoyan and T. Ye. Romanova 107 Generalized Interval Arithmetic J. Tupper 108 The Evaluation of Effectiveness of a Method of Solving the Interval Systems of Algebraic Equations and their Applications N. M. Vasilega and G. N. Gaponenko 109 Verification of Floating-Point Arithmetic D. Verschaeren 110 A Stopping Criterion for Rootfinding Methods M. N. Vrahatis and D. G. Sotiropoulos 111 Intervals and other Fortran 2000 Requirements for Scientific Computing W. Walter 112 H-infinity-control using Polynomial Matrices and Interval Arithmetic J. K. Weinhofer and W. C. Haas 113 Verified Computation of the Jacobi-Functions K. Werner 114 Computer Assisted Proof of Chaos for Lorenz System. Part I. TS-maps. P. Zgliczynski and Z. Galias 116

Solving Algebraic Equations on Intervals B. M. Acioly 117 Verified Solving on Nonlinear Algebraic Systems in Maple N. S. Dimitrova 119 On Interval Mathematical Assistant N. G. Glazunov 121 Interval Arithmetic and Parallelism C. L. Hoeher, L. G. L. Fernandes, P. W. de Oliveira, T. A. Diverio, and P. O. A. Navaux 123 Interval Analysis Algorithms for Robust Absolute Stability L. Kolev, D. Valtchev, and V. Borshukova 125 Design of Efficient Reusable Software Components for Scientific Computing M. Lerch 127 Interval Linear Programming V. I. Levin 129 Some Aspects of Interval Geometry Yu. G. Stoyan 130 Interval and Multiinterval Extensions in Subdefinite Models V. Telerman, V. Sidorov, and D. Ushakov 131 Approximation of Function by Algebraic Polynomials Close to the Best Ones V. S. Zyuzin 133 A Method of Estimating the Solution of a System of Ordinary Differential Equations by Using Lemniscate V. S. Zyuzin and N. A. Novikova 134 Author Index 135

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Foreword 1 - 4 Inclusion of Zeros of Nowhere Differentiable n-Dimensional Functions Siegfried M. Rump 5 - 16 Sharpness in Interval Computations Eldon R. Hansen 17 - 29 An Interval Algorithm for Bounding the Ranges of Real-Valued Functions of One Real Variable Michael A. Wolfe 31 - 50 NP-Hard Classes of Linear Algebraic Systems with Uncertainties Anatoly V. Lakeyev and Vladik Kreinovich 51 - 81 Use of Interval Slopes for the Irrational Part of Factorable Functions Lubomir V. Kolev 83 - 93 From Numerical Intervals to Set Intervals (Interval-Related Results Presented at the First International Workshop on Applications and Theory of Random Sets) Hung T. Nguyen and Vladik Kreinovich 95 - 102Back to the Table of Contents of "Reliable Computing"

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Algebraic Approach in the ``Outer Problem'' for Interval Linear Equations Sergey P. Shary 103 - 135 Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case Teruya Minamoto and Mitsuhiro T. Nakao 137 - 147 Is Solar System Stable? A Remark Vladik Kreinovich and Andrew Bernat 149 - 154 Computing the Value of a Boolean Expression with Interval Inputs is NP-Hard Leticia S. Chee 155 - 172 Sign-Stable Solutions of Column-Vague Linear Equation Systems Josef Nedoma 173 - 180 Reviews Applications of Reliable Scientific Computing 181 - 187 Information on New Textbooks 188 - 190 Interval-Related Talks at the 1996 International Workshop on Control Mechanisms for Complex Systems 191 - 193Back to the Table of Contents of "Reliable Computing"

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Foreword 195 - 198

S. Markov Isomorphic Embeddings of Abstract Interval Systems 199 - 207 Z. Kulpa Diagrammatic Representation of Interval Space in Proving Theorems about Interval Relations 209 - 217 D. Berthelot and M. Daumas Computing on Sequences of Embedded Intervals 219 - 227 J. Weinhofer and W. Haas $H_\infty$-Control using Polynomial Matrices and Interval Arithmetic 229 - 237

W. Hofschuster and W. Kraemer A Computer Oriented Approach to Get Sharp Reliable Error Bounds 239 - 248 W. Otten and W. Luther Approximation Error and Error Accumulation for the Landen Transform 249 - 258 C. Bliek Fast Evaluation of Partial Derivatives and Interval Slopes 259 - 268 O. Caprani, K. Madsen, and O. Stauning Existence Test for Asynchronous Interval Iteration 269 - 275 M. Mrozek and M. Zelawski Heteroclinic connections in the Kuramoto-Sivashinsky equation: a computer assisted proof 277 - 285 H.-J. Dobner and S. Ritter Attacking a conjecture in mathematical physics by combining methods of computational analysis and scientific computing 287 - 295 B. Dobronets Two-sided Multigrid Method for Elliptic Boundary Value Problems 297 - 303

B. Acioly and B. Bedregal A Quasi-Metric Topology Compatible with Inclusion Monotonicity on Interval Space 305 - 313 J. Rohn Complexity of Some Linear Problems with Interval Data 315 - 323 M. Rueher and C. Solnon Concurent Cooperating Solvers on the Reals 325 - 333 F. Benhamou and L. Granvilliers Automatic Generation of Numerical Redundancies for Non-Linear Constraint Solving 335 - 344

Interval'98 First announcement and call for papers 345 - 347Back to the Table of Contents of "Reliable Computing"

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Slope Methods of Higher Order for the Inclusion of Complex Roots of Polynomials Ljiljana D. Petkovic, Slobodan Trickovic, and Miodrag S. Petkovic 349 - 362 On Overestimations Produced by the Interval Gaussian Algorithm (Dedicated to Prof. Dr. Gerhard Heindl on the occasion of his 60th birthday) Jiri Rohn 363 - 368 Interval and Twin Arithmetics Vyacheslav M. Nesterov 369 - 380 Finding Global Minima of Maximum Functions by Using Exclusion Functions without Derivatives Ferenc Kalovics and Gabriella Meszaros 381 - 399 A New Approach to the Modal Regulator Synthesis for Interval Plant with Scalar Input Yelena M. Smagina 401 - 410 Error Reduction of the Taylor Centered Form by Half and an Inner Estimation of the Range Volker Stahl 411 - 420 How to Compute Interval Inclusions of Geodetic Coordinates from Interval Inclusions of Cartesian Coordinates Gerhard Heindl 421 - 435 On a Theoretical Justification of the Choice of Epsilon-Inflation in PASCAL-XSC Vladik Kreinovich, Scott Starks, and Guenter Mayer 437 - 445 Reviews: Applications of Reliable Scientific Computing 447 - 452 Interval and Complexity Workshops Back-to-Back with 1997 ACM Symposium on Theory of Computing (STOC'97) Luc Longpre and Martin Berz 453 - 457 Interval-Related Talks at NASA URC Conference Monica Nogueira 459 - 460 Reliable Computing Special Issue on Reliable Geometric Computations Co-editors: H. Ratschek and J. Rokne 461 - 462 Best Paper Award to Zdzislaw Pawlak 463 Patrick Suppes is 75 464Back to the Table of Contents of "Reliable Computing"

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Foreword 1 - 2

Bounds for the Range of a Bivariate Polynomial over a Triangle Ralf Hungerbuehler and Juergen Garloff 3 - 13 An Interval Entropy Penalty Method for Nonlinear Global Optimization Huang Zhenyu 15 - 25 An Interval Polynomial Interpolation Problem and Its Lagrange Solution Chenyi Hu, Angelina Cardenas, Stephanie Hoogendoorn, and Pedro Sepulveda Jr. 27 - 38 Algorithms That Still Produce a Solution (Maybe Not Optimal) Even When Interrupted: Shary's Idea Justified Maria Beltran, Gilbert Castillo, and Vladik Kreinovich 39 - 53

Interval Methods in Robot Navigation David Morales and Tran Cao Son 55 - 61 Reliable Optimal Production Control with Cobb-Douglas Model Zhihui Huey Hu 63 - 69

A Software Tool for Automatically Verified Operations on Intervals and Probability Distributions Daniel Berleant, Hang Cheng 71 - 82 Computation and Application of Taylor Polynomials with Interval Remainder Bounds Martin Berz and Georg Hoffstaetter 83 - 97

A New Application of Local Minima of Interval Functions: Interval-Valued Fuzzy Control Clifton Davis 99 - 101 Intervals Help to Design an Imaging System Graciela Gonzalez 103 - 104

A Brief Description of Gell-Mann's Lecture and How Intervals May Help to Describe Complexity in the Real World Misha Koshelev and Luc Longpr'e 105 - 107 Intervals in Space-Time: A. D. Alexandrov is 85 Alexander Levichev and Olga Kosheleva 109 - 112

Reliable Computing Special Issue on Applications to Control, Signals, and Systems 113 - 114Back to the Table of Contents of "Reliable Computing"

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Constructive L^2 Error Estimates for Finite Element Solutions of the Stokes Equations Mitsuhiro T. Nakao, Nobito Yamamoto, and Yoshitaka Watanabe 115 - 124 A New Method for Global Solution of Systems of Non-Linear Equations Lubomir V. Kolev 125 - 146 Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals Daniel Berleant and Chaim Goodman-Strauss 147 - 165 A Relation Between Morphological and Interval Operations Antony T. Popov 167 - 178 When Is the Product of Intervals Also an Interval? Olga Kosheleva and Piet G. Vroegindeweij 179 - 190

Intervals and the Origins of Calculus David Dennis, Vladik Kreinovich, and Siegfried M. Rump 191 - 197

One Criterion of Existence of a Hamiltonian Cycle Anatoly D. Plotnikov 199 - 202

SCAN'97 203 - 204Back to the Table of Contents of "Reliable Computing"

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On the Applicability of the Interval Gaussian Algorithm Guenter Mayer and Jiri Rohn 205 - 222 On a Second Derivative Test due to Qi Michael A. Wolfe 223 - 234 Universal Approximation Theorem for Interval Neural Networks Mark R. Baker and Rajendra B. Patil 235 - 239

Estimating Uncertainties for Geophysical Tomography Diane I. Doser, Kevin D. Crain, Mark R. Baker, Vladik Kreinovich, and Matthew C. Gerstenberger 241 - 268 The Use of Interval Analysis in Hydrologic Systems Tiraz R. Birdie and Karan S. Surana 269 - 281 An Application of Fuzzy Mathematical Morphology to Interval-Valued Knowledge Representation: A Remark Antony T. Popov, Hung T. Nguyen, and Leonid K. Reznik 283 - 290 Interval + Image = Wavelet: For Image Processing under Interval Uncertainty, Wavelets Are Optimal Alejandro E. Brito and Olga Kosheleva 291 - 301

Exclusive OR Operation That Leads to the Narrowest Intervals Alfredo Gabaldon and Hung T. Nguyen 303 - 306

Review of the book O.Aberth: Precise Numerical Methods Using C++, Academic Press, 1998 307 - 308

International Conference Interval'98 309Back to the Table of Contents of "Reliable Computing"

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Wrapping Effect and Wrapping Function Roumen Anguelov and Svetoslav Markov 311 - 330 Reliable Collision Detection for Time-Dependent Parametric Surfaces Anthony Leclerc and Jeff Ely 331 - 344 An NP-Hardness Result for Nonlinear Systems Christian Jansson 345 - 350 Optimal Enclosure of Quadratic Interval Functions Misha Koshelev, Luc Longpre, and Patrick Taillibert 351 - 360 Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models Martin Berz and Kyoko Makino 361 - 369

A Note on Epsilon-Inflation Siegfried M. Rump 371 - 375

Intersection Subdistributivity and Interval Hull Superdistributivity with Respect to the Interval Maps Gregory G. Menshikov 377 - 381 Solving Linear Interval Systems Is NP-Hard Even If We Exclude Overflow and Underflow Gerhard Heindl, Vladik Kreinovich, and Anatoly V. Lakeyev 383 - 388 Why Intervals? Because If We Allow Other Sets, Tractable Problems Become Intractable Monica Nogueira, Amarendra Nandigam 389 - 394

Hyper-Spectral Satellite Images: Interval Methods May Be Helpful Erzsebet Merenyi, Scott Starks, and Karen Villaverde 395 - 397 Hilbert Problems (Almost) 100 Years Later (From the Viewpoint of Interval Computations) Olga M. Kosheleva 399 - 403

Review of the book V. Kreinovich, A. Lakeyev, J. Rohn, and P. Kahl, Computational Complexity and Feasibility of Data Procesing and Interval Computations. Kluwer Academic Publishers, Dordrecht etc., 1998 405 - 409

1998 SIAM Annual Meeting: Interval Highlights 411 - 412 ICRA99 International Conference on Rational Approximation 413 - 414Back to the Table of Contents of "Reliable Computing"

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Preface 1 Efficient Control of the Dependency Problem Based on Taylor Model Methods Kyoko Makino and Martin Berz 3 - 12 New Methods for High-Dimensional Verified Quadrature Martin Berz and Kyoko Makino 13 - 22 Solving Underdetermined Systems with Interval Methods Zhang Danqing, Li Weiguo and Shen Zuhe 23 - 33 Representing Knowledge within the Situation Calculus Using Interval-Valued Epistemic Fluents John Funge 35 - 61 How to Guarantee Finite Termination of Verifying Global Optimization Codes Gerhard Heindl 63 - 68 Expression Templates for Dot Product Expressions Michael Lerch and Juergen Wolff von Gudenberg 69 - 80 Error Estimation for Indirect Measurements: Interval Computation Problem Is (Slightly) Harder Than a Similar Probabilistic Computational Problem Olga Kosheleva and Vladik Kreinovich 81 - 95

NMA'98 97 - 100 SCAN'98 101 - 102Back to the Table of Contents of "Reliable Computing"

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An Improved Method for Global Solution of Non-Linear Systems Lubomir V. Kolev 103 - 111 Rigorous Numerical Approach to Isolation in Dynamical Systems on the Example of the Kuramoto-Sivashinsky Equation Marcin Zelawski 113 - 129 A Simple Derivation of the Hansen-Bliek-Rohn-Ning-Kearfott Enclosure for Linear Interval Equations Arnold Neumaier 131 - 136 Computing Exact Bounds on Elements of an Inverse Interval Matrix is NP-Hard Gregory E. Coxson 137 - 142 Wrapping Function of the Initial Value Problem for ODE: Applications Roumen Anguelov 143 - 164 Estimation of Discrete-Event Systems Using Interval Computation Luc Jaulin, Jean-Louis Boimond, Laurent Hardouin 165 - 173

Interval Estimates for Signal Processing: Special Purpose Hardware Olga Kosheleva, Sergio D. Cabrera, Glenn A. Gibson, Sreedhar Cherukuri 175 - 196

Interval Computations Help in Proving the Kepler Conjecture 197 - 199 Review of the book "Bounded Queries in Recursion Theory" by W. I. Gasarch and G. A. Martin 201 - 203

Karl Nickel is turned 75 205 - 206 Interval Workshop MISC'99 207 - 208 Reminiscences "Back in the Good Old Days..." 209Back to the Table of Contents of "Reliable Computing"

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Preface 211 - 212 Comparing Partial Consistencies Helene Collavizza, Francois Delobel, and Michel Rueher 213 - 228 Verified Computation of Fast Decreasing Polynomials Neli S. Dimitrova and Svetoslav M. Markov 229 - 240 An Accurate Distance-Calculation Algorithm for Convex Polyhedra Eva Dyllong, Wolfram Luther, and Werner Otten 241 - 253 Verified Error Bounds for Linear Systems Through the Lanczos Process Andreas Frommer and Andre Weinberg 255 - 267 A Representation of the Interval Hull of a Tolerance Polyhedron Describing Inclusions of Function Values and Slopes Gerhard Heindl 269 - 278 A Few Results on Table-Based Methods Jean-Michel Muller 279 - 288 An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation Nedialko S. Nedialkov and Kenneth R. Jackson 289 - 310 The Interval-Enhanced GNU Fortran Compiler Michael J. Schulte, Vitaly Zelov, Ahmet Akkas, and James Craig Burley 311 - 322 Outer Estimation of Generalized Solution Sets to Interval Linear Systems Sergey P. Shary 323 - 335 A Real Polynomial Decision Algorithm Using Arbitrary-Precision Floating Point Arithmetic Adam Strzebonski 337 - 346 A Numerical Verification Method of Solutions for the Navier-Stokes Equations Yoshitaka Watanabe, Nobito Yamamoto, and Mitsuhiro T. Nakao 347 - 357Back to the Table of Contents of "Reliable Computing"

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On the Componentwise Krawczyk-Moore Iteration Kong Min, Liu Qi, and Shen Zuhe 359 - 370 On Discrete Minimax Problems in R Using Interval Arithmetic Michael A. Wolfe 371 - 383 Only Intervals Preserve the Invertibility of Arithmetic Operations Olga Kosheleva and Vladik Kreinovich 385 - 394 Solving Nonlinear Constrained Minimization Problems with a New Interval Valued Function Ferenc Kalovics 395 - 406

Synthesis of Robustly Stabilizing General Order Compensators for Interval Plants Using Interval Analysis Paluri S. V. Nataraj and Suresh Srivastava 407 - 422

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The Dawning Ramon Moore 423 - 424Back to the Table of Contents of "Reliable Computing"

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Introduction to the Special Issue: What Can One Learn from Box-Plane Intersections? Helmut Ratschek and Jon G. Rokne 1 - 8 Robust and Efficient Ray Intersection of Implicit Surfaces Ole Caprani, Lars Hvidegaard, Mikkel Mortensen, and Thomas Schneider 9 - 21 Correct Delaunay Triangulation in the Presence of Inexact Inputs and Arithmetic Jeffrey S. Ely and Anthony P. Leclerc 23 - 38 Exact Computation of Delaunay and Power Triangulations Marina Gavrilova, Helmut Ratschek, and Jon G. Rokne 39 - 60 Removing Degeneracies by Perturbing the Problem or Perturbing the World Pierre Alliez, Olivier Devillers, and Jack Snoeyink 61 - 79 Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations Timothy J. Hickey, Zhe Qiu, and Maarten H. van Emden 81 - 92

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Interval Integration L. B. Rall 93 - 94Back to the Table of Contents of "Reliable Computing"

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The Hull of Preconditioned Interval Linear Equations Eldon R. Hansen 95 - 103 Finding All Solutions of Nonlinear Equations Using Linear Combinations of Functions Kiyotaka Yamamura 105 - 113 Computation of the Bernstein Coefficients on Subdivided Triangles Ralf Hungerbuehler and Juergen Garloff 115 - 121 Jacobi and Gauss-Seidel Iterations for Polytopic Systems: Convergence via Convex M-Matrices Dusan M. Stipanovic and Dragoslav D. Siljak 123 - 137 A Coherence Space of Rational Intervals for a Construction of IR Gracaliz P. Dimuro, Antonio Carlos da R. Costa, and Dalcidio M. Claudio 139 - 178 Interval Branch and Bound Algorithm for Finding the First-Zero-Crossing-Point in One-Dimensional Functions Leocadio G. Casado, Inmaculada F. Garcia, and Yaroslav D. Sergeyev 179 - 191 Accelerated Shift-and-Add Algorithms Nathalie Revol and Jean-Claude Yakoubsohn 193 - 205 Mathematical Function Software on the Web - Are Such Codes Useful for Verification Algorithms? Werner Hofschuster and Walter Kraemer 207 - 218 Every Superinterval of the Function Range Can Be an Interval-Computations Enclosure Misha Koshelev 219 - 223 Reminiscences Eldon R. Hansen 225 Erratum to: A Simple Derivation of the Hansen-Bliek-Rohn-Ning-Kearfott Enclosure for Linear Interval Equations (Reliable Computing Vol. 5 (2) (1999)) Arnold Neumaier 227Back to the Table of Contents of "Reliable Computing"

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Foreword 229 - 230 Composite Interval Control Systems: Some Strong Kharitonov-Like Properties Long Wang 231 - 246 Nonconvex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control Systems Yuzo Ohta 247 - 279 Analysis of the Robustness of Predictive Controllers via Modal Intervals Josep Vehi, Jose Rodellar, Miguel Sainz, and Joaquim Armengol 281 - 301 Application of Bernstein Expansion to the Solution of Control Problems Juergen Garloff 303 - 320 Interval Methods for Sinusoidal Parameter Estimation: A Comparative Analysis William W. Edmonson, Wen H. Lee, and John M. M. Anderson 321 - 336 Robust Autonomous Robot Localization Using Interval Analysis Michel Kieffer, Luc Jaulin, Eric Walter, and Dominique Meizel 337 - 361Back to the Table of Contents of "Reliable Computing"

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Foreword 363 Effective Computation of Rational Approximants and Interpolants Bernhard Beckermann and George Labahn 365 - 390 Rational Interpolation from Stochastic Data: A New Froissart's Phenomenon Jean-Daniel Fournier and Maciej Pindor 391 - 409 Reliability of Lanczos-Type Product Methods from Perturbation Theory Peter R. Graves-Morris 411 - 428 Hybrid Rational Function Approximation and Its Accuracy Analysis Hiroshi Kai and Matu-Tarow Noda 429 - 438 Numerical Computation of the Least Common Multiple of a Set of Polynomials Nicos Karcanias and Marilena Mitrouli 439 - 457 On Factorization of Analytic Functions and Its Verification Tetsuya Sakurai and Hiroshi Sugiura 459 - 470Back to the Table of Contents of "Reliable Computing"

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Path Planning Using Intervals and Graphs Luc Jaulin 1 - 15 Automatic Computation of a Linear Interval Enclosure Lubomir V. Kolev 17 - 28 On Kernel Inclusions Hans-Juergen Dobner 29 - 39 Roundoff-Free Number Fields for Interval Computations Vladik Kreinovich 41 - 47

A Note on a Uniqueness Theorem for the Second-Derivative Test of Qi Michael A. Wolfe 49 - 52 On /\-Subdistributivity and \/-Superdistributivity with Respect to Interval Map in Kaucher Arithmetic Gregory G. Menshikov, Alexey V. Tomashevsky 53 - 57 The Feasibility of the Interval Gaussian Algorithm for Arrowhead Matrices Uwe Schaefer 59 - 62

The Mystery of Intervals Svetoslav Markov 63 - 65

Interval Methods and Their Applications: invited sessions at the World Automation Congress (WAC'2000) 67 - 68 Session "Interval and Computer-Algebraic Methods in Science and Engineering" at the 6th International Association for Mathematics and Computers in Simulation (IMACS) Conference on Applications of Computer Algebra (ACA'2000) 69 - 70 A special session on Granular Computing and Interval Computations at the 19th International Conference of the North American Fuzzy Information Processing Society (NAFIPS) 71 - 72 Minisymposium on Applications of Interval Computations at the Third World Congress of Nonlinear Analysts 73 - 74Back to the Table of Contents of "Reliable Computing"

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Foreword 75 Modal Intervals Ernest Gardenes, Miguel A. Sainz, Lambert Jorba, Remei Calm, Rosa Estela, Honorino Mielgo, and Albert Trepat 77 - 111 On the Algebraic Properties of Intervals and Some Applications Svetoslav Markov 113 - 127 Multiplication Distributivity of Proper and Improper Intervals Evgenija D. Popova 129 - 140 Interval Gauss-Seidel Method for Generalized Solution Sets to Interval Linear Systems Sergey P. Shary 141 - 155 A Limitation for Underestimation via Twin Arithmetic Peter Hertling 157 - 169 Application of Modal Intervals to the Generation of Error-Bounded Envelopes Joaquim Armengol, Josep Vehi, Louise Trave-Massuyes, and Miguel Angel Sainz 171 - 185

SCAN 2000: GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics Interval 2000: International Conference on Interval Methods in Science and Engineering 187 - 191Back to the Table of Contents of "Reliable Computing"

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Foreword 193 - 194

On Bounding Solutions of Underdetermined Systems Michael A. Wolfe 195 - 207 On The Theory of Error Control Based on Moduli with Common Factors Andraos Sweidan, Amman, Jordan, and Ahmad A. Hiasat 209 - 218 Robust Control Using Interval Analysis Vladimir N. Shashikhin 219 - 230 Reliable Minimax Parameter Estimation Luc Jaulin 231 - 246 Spigot Algorithm and Root Computing Dang-Khoa Do 247 - 273

A Comment on the Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients Goetz Alefeld, Vladik Kreinovich, Guenter Mayer, and Michael Huth 275 - 277

Interval talks at the International Conference on Intelligent Technologies InTech'2000 279 - 280Back to the Table of Contents of "Reliable Computing"

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Synchronous and Asynchronous Interval Newton-Schwarz Methods for a Class of Large Systems of Nonlinear Equations Hartmut Schwandt 281 - 306 Validated Bounds for Taylor Coefficients of Analytic Functions Markus Neher 307 - 319

Automatic Forward Error Analysis for Floating Point Algorithms Walter Kraemer and Armin Bantle 321 - 340

Interval Methods in Non-Destructive Testing of Material Structures Keith Worden, Roberto Osegueda, Carlos Ferregut, Soheil Nazarian, Debra L. George, Mary J. George, Vladik Kreinovich, Olga Kosheleva, and Sergio Cabrera 341 - 352Back to the Table of Contents of "Reliable Computing"

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Idempotent Interval Analysis and Optimization Problems Grigori L. Litvinov and Andrei N. Sobolevskii 353 - 377 Verified High-Order Inversion of Functional Dependencies and Interval Newton Methods Martin Berz and Jens Hoefkens 379 - 398 Cheap and Tight Bounds on the Solution Set of Perturbed Systems of Nonlinear Equations Lubomir V. Kolev and Ivo P. Nenov 399 - 408 On Maximal Inner Estimation of the Solution Sets of Linear Systems with Interval Parameters Irene A. Sharaya 409 - 424

An Example of Singularity in Nonlinear Systems R. Baker Kearfott 425 - 429 Claude E. Shannon (1916-2001) 431 - 432Back to the Table of Contents of "Reliable Computing"

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Linear Interval Tolerance Problem and Linear Programming Techniques Oliver Beaumont and Bernard Philippe 433 - 447 An Effective High-Order Interval Method for Validating Existence and Uniqueness of the Solution of an IVP for an ODE Nedialko S. Nedialkov, Kenneth R. Jackson, and John D. Pryce 449 - 465 On the Combination of Interval Constraint Solvers Laurent Granvilliers 467 - 483 The Preliminary Enclosing of the ODE Solutions on the Base of the Cauchy-Duhamel Identity Gregory G. Menshikov 485 - 495 A Surprising Approach in Interval Global Optimization Sergey P. Shary 497 - 505

Gregory G. Menshikov has turned 70 507 - 508 SCAN 2002 509 - 510Back to the Table of Contents of "Reliable Computing"

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Two Ways to Extend the Cholesky Decomposition to Block Matrices with Interval Entries Uwe Schaefer 1 - 20 Approximate Quantified Constraint Solving by Cylindrical Box Decomposition Stefan Ratschan 21 - 42 Exact Minkowski Products of N Complex Disks Rida T. Farouki, Helmut Pottmann 43 - 66 Verification of Invertibility of Complicated Functions over Large Domains Jens Hoefkens, Martin Berz 67 - 82 A New Subdivision Strategy for Range Computations Paluri S. V. Nataraj, Suresh Mandir Sheela 83 - 92

Special Issue on the Linkages Between Interval Mathematics and Fuzzy Set Theory 93 - 95Back to the Table of Contents of "Reliable Computing"

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Interval-Valued Finite Markov Chains Igor O. Kozine and Lev V. Utkin 97 - 113 Sharp Bounds on Interval Polynomial Roots Eldon R. Hansen and G. William Walster 115 - 122

A Parallelized Version of the Covering Algorithm for Solving Parameter-Dependent Systems of Nonlinear Equations Paluri S. V. Nataraj and Airani Kalathil Prakash 123 - 130 Interval Computation of Viswanath's Constant Joao Batista Oliveira and Luiz Henrique de Figueiredo 131 - 138

Efficient Interval Linear Equality Solving in Constraint Logic Programming Chong-Kan Chiu and Jimmy Ho-Man Lee 139 - 174

Reliable Computing: Special Issue on Dependable Reasoning about Uncertainty Daniel Berleant 175 - 176Back to the Table of Contents of "Reliable Computing"

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Bounding Perturbations in Zeros of Nonlinear Systems Michael A. Wolfe 177 - 188 Formal Solution to Systems of Interval Linear or Non-Linear Equations Miguel A. Sainz, Ernest Gardenyes, and Lambert Jorba 189 - 211 In Case of Interval (or More General) Uncertainty, No Algorithm Can Choose the Simplest Representative Gerhard Heindl, Vladik Kreinovich, and Maria Rifqi 213 - 227 An Approach to Overcome Division by Zero in the Interval Gauss Algorithm Jan Mayer 229 - 237 Intervals of Inverse M-matrices Charles R. Johnson and Ronald L. Smith 239 - 243

Rump's Example Revisited Eugene Loh and G. William Walster 245 - 248Back to the Table of Contents of "Reliable Computing"

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Sparse Systems in Fixed Point Form Ramon E. Moore 249 - 265 On Existence and Uniqueness Verification for Non-Smooth Functions R. Baker Kearfott 267 - 282 Interval Estimations of Solution Sets to Real-Valued Systems of Linear or Non-Linear Equations Miguel A. Sainz, Ernest Gardenyes, and Lambert Jorba 283 - 305

Interval Arithmetic on Multimedia Architectures Juergen Wolff von Gudenberg 307 - 312

Grand Challenges and Scientific Standards in Interval Analysis Arnold Neumaier 313 - 320Back to the Table of Contents of "Reliable Computing"

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A New Technique in Systems Analysis under Interval Uncertainty and Ambiguity Sergey P. Shary 321 - 418

SIAM Conference on Optimization, Validated Computing 2002, and the Fields Institute Informal Working Group on Validated Optimization 419 - 424 Interval-Related Talks at the Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'02 425 - 426Back to the Table of Contents of "Reliable Computing"

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A QFT Procedure for Generating Design Frequencies and Bounds of Guaranteed Accuracy Paluri S. V. Nataraj and Suresh Mandir Sheela 427 - 451 Symbolic Preconditioning with Taylor Models: Some Examples R. Baker Kearfott and G. William Walster 453 - 468 Kernel-Splitting Technique for Enclosing the Solution of Fredholm Equations of the First Kind Hans-Juergen Dobner 469 - 479 Range Estimation Is NP-Hard for e^2 Accuracy and Feasible for e^(2-d) Vladik Kreinovich 481 - 491 Outer Solution of Linear Systems Whose Elements Are Affine Functions of Interval Parameters Lubomir V. Kolev 493 - 501

Epistemic Uncertainty Workshop 503 - 505Back to the Table of Contents of "Reliable Computing"

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Diagrammatic Analysis of Interval Linear Equations: Part I: Basic Notions and the One-Dimensional Case Zenon Kulpa 1 - 20 Controlling the Wrapping Effect in the Solution of ODEs for Asteroids Jens Hoefkens, Martin Berz, and Kyoko Makino 21 - 41

Taylor Forms - Use and Limits Arnold Neumaier 43 - 79

COCOS'02: A Workshop on Global Constrained Optimization and Constraint Satisfaction R. Baker Kearfott 81 - 87Back to the Table of Contents of "Reliable Computing"

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Preface 89 - 90 Statool: A Tool for Distribution Envelope Determination (DEnv), an Interval-Based Algorithm for Arithmetic on Random Variables Daniel Berleant, Lizhi Xie, Jianzhong Zhang 91 - 108 Numerical Experiences with a New Generalized Subinterval Selection Criterion for Interval Global Optimization Tibor Csendes 109 - 125 Estimating and Validating the Cumulative Distribution of a Function of Random Variables: Toward the Development of Distribution Arithmetic Weldon A. Lodwick, K. David Jamison 127 - 141 Interval Methods for Accelerated Global Search in the Microsoft Excel Solver Ivo P. Nenov, Daniel H. Fylstra 143 - 159 Robust Approximation of Offsets, Bisectors, and Medial Axes of Plane Curves Joao Batista Oliveira, Luiz Henrique de Figueiredo 161 - 175 Evaluation of Functions, Gradients, and Jacobians Louis B. Rall 177 - 182

SCAN'2002 183 - 184Back to the Table of Contents of "Reliable Computing"

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Higher Order Convergence for Multidimensional Functions with a New Taylor-Bernstein Form as Inclusion Function Paluri S. V. Nataraj, Ketan Kotecha 185 - 203 Diagrammatic Analysis of Interval Linear Equations. Part II: The Two-Dimensional Case and Generalization to n Dimensions Zenon Kulpa 205 - 228 Computation of Sharp Rigorous Componentwise Error Bounds for the Approximate Solutions of Systems of Linear Equations Takeshi Ogita, Shin'ichi Oishi, Yasunori Ushiro 229 - 239

Finding All Solution Sets of Piecewise-Trapezoidal Equations Described by Set-Valued Functions Kiyotaka Yamamura 241 - 250Back to the Table of Contents of "Reliable Computing"

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Worst-Case Simulation of Discrete Linear Time-Invariant Interval Dynamic Systems Vicenc Puig, Jordi Saludes, and Joseba Quevedo 251 - 290 Optimal Bicentered Form Youkang Fang 291 - 302 Asymptotic Stability of Interval Time-Delay Systems Svetlana P. Sokolova and Ruslan S. Ivlev 303 - 313Back to the Table of Contents of "Reliable Computing"

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Preface 315 Interval Global Optimization in Solvent Design Luke E. K. Achenie and Manish Sinha 317 - 338 Extended Interval Power Function Walter Kraemer and Juergen Wolff von Gudenberg 339 - 347 Are There Easy-to-Check Necessary and Sufficient Conditions for Straightforward Interval Computations To Be Exact? Vladik Kreinovich, Luc Longpre, and James J. Buckley 349 - 358 Some Computer Assisted Proofs for Solutions of the Heat Convection Problems Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, and Takaaki Nishida 359 - 372 Reliable Computation of Frequency Response Plots for Nonrational Transfer Functions to Prescribed Accuracy Paluri S. V. Nataraj and Jayesh J. Barve 373 - 389 Accelerated Enclosure Methods for Ordinary Free Boundary Problems Uwe Schaefer 391 - 403

Interval-Related Talks at the 2003 IEEE International Conference on Fuzzy Systems 405 - 406Back to the Table of Contents of "Reliable Computing"

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Dependable Handling of Uncertainty Daniel Berleant, Mei-Peng Cheong, Chris Chu, Yong Guan, Ahmed Kamal, Gerald Sheble, Scott Ferson, and James F. Peters 407 - 418 Computation of Bounds on Population Parameters When the Data Are Incomplete Joel L. Horowitz, Charles F. Manski, Maria Ponomareva, and Joerg Stoye 419 - 440 Exact Upper Bound on the Mean of the Product of Many Random Variables with Known Expectations Vladik Kreinovich, Scott Ferson, and Lev Ginzburg 441 - 463 Convex Imprecise Previsions Renato Pelessoni and Paolo Vicig 465 - 485 Tree-Based Credal Networks for Classification Marco Zaffalon and Enrico Fagiuoli 487 - 509Back to the Table of Contents of "Reliable Computing"

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Set Computation for Nonlinear Control Luc Jaulin, Stefan Ratschan, and Laurent Hardouin 1 - 26 Global Optimization with Higher Order Inclusion Function Forms. Part 1: A Combined Taylor-Bernstein Form Paluri S. V. Nataraj and Ketan Kotecha 27 - 44 On the Significance of Digits in Interval Notation Maarten H. van Emden 45 - 58

Special Session "Set-Valued Numerics and Reliable Computing" 59 - 61 Interval-Related Talks at the 4th International Conference on Frontiers in Global Optimization 63 - 70 Interval-Related Talks at the 22th International Conference of the North American Fuzzy Information Processing Society NAFIPS'03 71 - 73 Computability and Complexity in Analysis (CCA). A View from Interval Computations 75 - 80Back to the Table of Contents of "Reliable Computing"

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Introduction 81 - 82 Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals Hung T. Nguyen, Vladik Kreinovich, and Luc Longpre 83 - 106 On the Use of Random Set Theory to Bracket the Results of Monte Carlo Simulations Fulvio Tonon 107 - 137 Using Pearson Correlation to Improve Envelopes around the Distributions of Functions Daniel Berleant and Jianzhong Zhang 139 - 161Back to the Table of Contents of "Reliable Computing"

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Slope Intervals, Generalized Gradients, Semigradients, Slant Derivatives, and Csets Humberto Munoz and R. Baker Kearfott 163 - 193 Integral Approximation of Rays and Verification of Feasibility Waltraud Huyer and Arnold Neumaier 195 - 207 On a Refined Analysis of Some Problems in Interval Arithmetic Using Real Number Complexity Theory Klaus Meer 209 - 225 A Method for Outer Interval Solution of Linear Parametric Systems Lubomir V. Kolev 227 - 239

Fast Multiplication of Interval Matrices (Interval Version of Strassen's Algorithm) Martine Ceberio and Vladik Kreinovich 241 - 243

Interval-Related Talks at InTech'03 245 - 246Back to the Table of Contents of "Reliable Computing"

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Introduction 247 - 248 Clouds, Fuzzy Sets, and Probability Intervals Arnold Neumaier 249 - 272 Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities Didier Dubois, Laurent Foulloy, Gilles Mauris, and Henri Prade 273 - 297 Characterization of Interval Fuzzy Logic Systems of Connectives by Group Transformations Ladislav J. Kohout and Eunjin Kim 299 - 334Back to the Table of Contents of "Reliable Computing"

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Introduction 247 - 248 Modeling Uncertain Sparse Data with Fuzzy B-splines Angelo Marcello Anile and Salvatore Spinella 335 - 355 Fuzzy Linear Programming with Interactive Uncertain Parameters Masahiro Inuiguchi and Tetsuzo Tanino 357 - 367 Application of Functional Intervals to the Response Evaluation of Linear Time-Invariant Systems with Fuzzy Input Jorge Bondia and Jesus Pico 369 - 387 Solutions for the Portfolio Selection Problem with Interval and Fuzzy Coefficients Masaaki Ida 389 - 400 Eliminating Duplicates under Interval and Fuzzy Uncertainty: An Asymptotically Optimal Algorithm and Its Geospatial Applications Roberto Torres, G. Randy Keller, Vladik Kreinovich, Luc Longpre, and Scott A. Starks 401 - 422Back to the Table of Contents of "Reliable Computing"

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Enclosing Solutions of Linear Complementarity Problems for H-matrices Goetz Alefeld, Zhengyu Wang, and Zuhe Shen 423 - 435 Ostrowski-like Method with Corrections for the Inclusion of Polynomial Zeros Miodrag S. Petkovic and Dusan M. Milosevic 437 - 467 Discrete Optimization Problems with Interval Data: Pareto Set of Solutions or Set of Weak Solutions? Galina Kozina 469 - 487 Spigot Algorithm and Reliable Computation of Natural Logarithm Dang-Khoa Do 489 - 500Back to the Table of Contents of "Reliable Computing"

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Contracting Optimally an Interval Matrix without Loosing Any Positive Semi-Definite Matrix Is a Tractable Problem Luc Jaulin and Didier Henrion 1 - 17 Computing System Reliability Given Interval-Valued Characteristics of the Components Lev V. Utkin and Igor O. Kozine 19 - 34 A Normal Form Supplement to the Oettli-Prager Theorem Jiri Rohn 35 - 39 Interval Schemes for Singularly Perturbed Initial Value Problems Abdelhay A. Salama and Emad Hamdy 41 - 58 Outlier Detection under Interval Uncertainty: Algorithmic Solvability and Computational Complexity Vladik Kreinovich, Luc Longpre, Praveen Patangay, Scott Ferson, and Lev Ginzburg 59 - 76 On the Proofs of Some Statements Concerning the Theorems of Kantorovich, Moore, and Miranda Marco Schnurr 77 - 85Back to the Table of Contents of "Reliable Computing"

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On the Solutions of the Interval System [x]=[A][x]+[b] Hans-Robert Arndt and Guenter Mayer 87 - 103 The Optimal Solution of an Interval System of Linear Algebraic Equations Marina Lyashko 105 - 127 Linear Interval Equations: Midpoint Preconditioning May Produce a 100% Overestimation for Arbitrarily Narrow Data Even in Case n=4 Jiri Rohn 129 - 135

Using Zonotopes for Overestimation-Free Interval Least-Squares -- Some Geodetic Applications Steffen Schoen and Hansjoerg Kutterer 137 - 155

SCAN'2004 11th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics 157 - 159 Second R. E. Moore Prize Awarded at SCAN'2004 161 - 162 Errata and Opinion to: "An Interval Entropy Penalty Method for Nonlinear Global Optimization," by Zhenyu Huang, Reliable Computing 4 (1) (1998) R. Baker Kearfott 163 - 164Back to the Table of Contents of "Reliable Computing"

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Enclosing Solutions of Singular Interval Systems Iteratively Goetz Alefeld and Guenter Mayer 165 - 190 Fast Inclusion of Interval Matrix Multiplication Takeshi Ogita and Shin'ichi Oishi 191 - 205 Exact Bounds on Finite Populations of Interval Data Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Luc Longpre, and Monica Aviles 207 - 233 Tolerances in Geometric Constraint Problems Johannes Wallner, Hans-Peter Schroecker, and Shi-Min Hu 235 - 251Back to the Table of Contents of "Reliable Computing"

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Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization Context Boglarka Toth and Tibor Csendes 253 - 273

Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library Nathalie Revol and Fabrice Rouillier 275 - 290 Checking If There Exists a Monotonic Function That Is Consistent with the Measurements: An Efficient Algorithm Kavitha Tupelly, Vladik Kreinovich, and Karen Villaverde 291 - 312 A Constructive Criticism of the C/C++ Proposal for Complex Arithmetic Franky Backeljauw and Annie Cuyt 313 - 319Back to the Table of Contents of "Reliable Computing"

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Preface 321 - 322 Interval-Affine Gaussian Algorithm for Constrained Systems Ramil R. Akhmerov 323 - 341 Developing Interval Global Optimization Algorithms on the Basis of Branch-and-Bound and Constraint Propagation Methods Yuri G. Dolgov 343 - 358 Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion Alexei G. Ershov and Tamara P. Kashevarova 359 - 367 Quantified Set Inversion Algorithm with Applications to Control Pau Herrero, Miguel A. Sainz, Josep Vehi, and Luc Jaulin 369 - 382 Validated Constraint Solving - Practicalities, Pitfalls, and New Developments R. Baker Kearfott 383 - 391 An Interval Global Optimization Algorithm Combining Symbolic Rewriting and Componentwise Newton Method Applied to Control a Class of Queueing Systems Bartlomiej Jacek Kubica and Krzysztof Malinowski 393 - 411 Boundary Realizations Method for Interval Linear Dynamic Systems Sergey G. Pushkov and Svetlana Yu. Kalinkina 413 - 423 On Unbounded Tolerable Solution Sets Irene A. Sharaya 425 - 432 On Fitting Empirical Data under Interval Error Sergei I. Zhilin 433 - 442Back to the Table of Contents of "Reliable Computing"

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A Right-Preconditioning Process for the Formal-Algebraic Approach to Inner and Outer Estimation of AE-Solution Sets Alexandre Goldsztejn 443 - 478 Optimal Finite Characterization of Linear Problems with Inexact Data Vladik Kreinovich 479 - 489

How Strong Is Strong Regularity? Jiri Rohn 491 - 493 A Theorem on Regularity of Interval Matrices Eldon Hansen 495 - 497

Reliable Computations and Their Applications 499 - 503Back to the Table of Contents of "Reliable Computing"

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Complex Interval Arithmetic Using Polar Form Yves Candau, Tarek Raissi, Nacim Ramdani, and Laurent Ibos 1 - 20 Sharpening Interval Computations Eldon Hansen 21 - 34 Interval Householder Method for Complex Linear Systems Bakyt S. Djanybekov 35 - 43

Robust Control for Two-Time-Scale Discrete Interval Systems Balasaheb M. Patre and Bijnan Bandyopadhyay 45 - 58 Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements Gang Xiang 59 - 64

Los Alamos National Laboratory Uncertainty Workshop: An Interval Perspective 65 - 71 Towards Real World Applications: Interval-Related Talks at NAFIPS'05 73 - 77Back to the Table of Contents of "Reliable Computing"

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A Contribution to the Feasibility of the Interval Gaussian Algorithm Guenter Mayer 79 - 98 Regularity of Interval Matrices and Theorems of the Alternatives Jiri Rohn 99 - 105 A Method for Outer Interval Solution of Systems of Linear Equations Depending Linearly on Interval Parameters Iwona Skalna 107 - 120 Outer Interval Solution of the Eigenvalue Problem under General Form Parametric Dependencies Lubomir V. Kolev 121 - 140

Efficient Task Scheduling in the Parallel Result-Verifying Solution of Nonlinear Systems Thomas Beelitz, Bruno Lang, and Christian H. Bischof 141 - 151

Dealing with Imprecise Probabilities: Interval-Related Talks at ISIPTA'05 153 - 165 Second Scandinavian Workshop on Interval Methods and Their Applications 167 - 169Back to the Table of Contents of "Reliable Computing"

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A General Reliable Quadratic Form: An Extension of Affine Arithmetic Frederic Messine and Ahmed Touhami 171 - 192 Improvement of a Direct Method for Outer Solution of Linear Parametric Systems Lubomir V. Kolev 193 - 202 Geometric Constructions with Discretized Random Variables Hans-Peter Schroecker and Johannes Wallner 203 - 223

Hardware Support for Interval Arithmetic Reinhard Kirchner and Ulrich W. Kulisch 225 - 237

Solving Overdetermined Systems of Interval Linear Equations Eldon Hansen and G. William Walster 239 - 243

Jiri Rohn 245 - 246

Interval-Related Talks at the International Conference on Fuzzy Systems, Neural Networks, and Genetic Algorithms FNG'05 247 - 251Back to the Table of Contents of "Reliable Computing"

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A Multidimensional Interval Newton Method Eldon Hansen 253 - 272 Population Variance under Interval Uncertainty: A New Algorithm Evgeny Dantsin, Vladik Kreinovich, Alexander Wolpert, and Gang Xiang 273 - 280 New Formulae for Multiplication of Intervals Lubomir V. Kolev 281 - 292

Modelling Geometric Objects and Tolerances with Intervals: Data Exchange with ISO Standard STEP Eva Dyllong, Wolfram Luther, and Holger Traczinski 293 - 302 Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library Christian Keil and Christian Jansson 303 - 321 Robust Plotting of Polar Algebraic Curves, Space Algebraic Curves, and Offsets of Planar Algebraic Curves Huahao Shou, Jie Shen, and David Yoon 323 - 335Back to the Table of Contents of "Reliable Computing"

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The Set of Hausdorff Continuous Functions - The Largest Linear Space of Interval Functions Roumen Anguelov, Svetoslav Markov, and Blagovest Sendov 337 - 363 Towards Optimal Use of Multi-Precision Arithmetic: A Remark Vladik Kreinovich and Siegfried Rump 365 - 369

Analysis and Design of Robust Controllers Using the Interval Diophantine Equation Alfredo D. S. Lordelo, Edvaldo A. Juzzo, and Paulo A. V. Ferreira 371 - 388 Parameter Reconstruction for Biochemical Networks Using Interval Analysis Warwick Tucker and Vincent Moulton 389 - 402Back to the Table of Contents of "Reliable Computing"

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Preface 403 - 404 Introductory Remarks on Reliable Engineering Computing Ramon E. Moore 405 - 408 Handling Uncertainty in the Development and Design of Chemical Processes David B. Johnson and I. David L. Bogle 409 - 426 Reliable Modeling and Optimization for Chemical Engineering Applications: Interval Analysis Approach Youdong Lin, C. Ryan Gwaltney, and Mark A. Stadtherr 427 - 450 Uncertainty in Thermal Basin Modeling: An Interval Finite Element Approach Sebastiao C. Pereira, Ulisses T. Mello, Nelson F. F. Ebecken, and Rafi L. Muhanna 451 - 470 Towards Combining Probabilistic and Interval Uncertainty in Engineering Calculations: Algorithms for Computing Statistics under Interval Uncertainty, and Their Computational Complexity Vladik Kreinovich, Gang Xiang, Scott A. Starks, Luc Longpr'e, Martine Ceberio, Roberto Araiza, Jan Beck, Raj Kandathi, Asis Nayak, Roberto Torres, and Janos G. Hajagos 471 - 501Back to the Table of Contents of "Reliable Computing"

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Experiments with Range Computations Using Extrapolation Nataraj S. V. Paluri and Shanta Sondur 1 - 23 Monte-Carlo-Type Techniques for Processing Interval Uncertainty, and Their Potential Engineering Applications Vladik Kreinovich, Jan Beck, Carlos Ferregut, Araceli Sanchez, G. Randy Keller, Matthew Averill, and Scott A. Starks 25 - 69 Interval Monte Carlo as an Alternative to Second-Order Sampling for Estimating Ecological Risk Janos G. Hajagos 71 - 81 Requirements Analysis for Engineering Computation: A Systematic Approach for Improving Reliability Spencer Smith, Lei Lai, and Ridha Khedri 83 - 107

Interval-Related Talks at the North American Fuzzy Information Processing Society Annual Conference NAFIPS'06 109 - 111 Interval-Related Talks at the Second International Conference on Fuzzy Sets and Soft Computing in Economics and Finance 113 - 117 Interval Talks at the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU'2006 119 - 124Back to the Table of Contents of "Reliable Computing"

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Formulation for Reliable Analysis of Structural Frames George Corliss, Christopher Foley, and R. Baker Kearfott 125 - 147 Linear Systems with Large Uncertainties, with Applications to Truss Structures Arnold Neumaier and Andrzej Pownuk 149 - 172 Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics Rafi L. Muhanna, Hao Zhang, and Robert L. Mullen 173 - 194 A Search Algorithm for Calculating Validated Reliability Bounds Fulvio Tonon 195 - 209 Solving Interval Constraints by Linearization in Computer-Aided Design Yan Wang and Bartholomew O. Nnaji 211 - 244Back to the Table of Contents of "Reliable Computing"

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On Interval Systems [x]=[A][x]+[b] and the Powers of Interval Matrices in Complex Interval Arithmetics Hans-Robert Arndt 245 - 259 Unimodality, Independence Lead to NP-Hardness of Interval Probability Problems Daniel J. Berleant, Olga Kosheleva, Vladik Kreinovich, and Hung T. Nguyen 261 - 282 Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity Ruslan S. Ivlev and Svetlana P. Sokolova 283 - 291 Bounds on Generalized Linear Predictors with Incomplete Outcome Data Joerg Stoye 293 - 302

Early Automatic Differentiation: The Ch'in-Horner Algorithm Louis B. Rall 303 - 308Back to the Table of Contents of "Reliable Computing"

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A New Robust Algorithm to Trace Curves Dominique Faudot and Dominique Michelucci 309 - 324 Extension of the Hansen-Bliek Method to Right-Quantified Linear Systems Gilles Chabert and Alexandre Goldsztejn 325 - 349 Guaranteed Parameter Set Estimation for Exponential Sums: The Three-Terms Case Juergen Garloff, Ismail Idriss, and Andrew P. Smith 351 - 359 Solution Set Characterization of Linear Interval Systems with a Specific Dependence Structure Milan Hladik 361 - 374

Interval-Related Talks at the International Conference on Finite Element Methods in Engineering and Science Vladik Kreinovich and Rafi Muhanna 375 - 379Back to the Table of Contents of "Reliable Computing"

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Guaranteeing the Homotopy Type of a Set Defined by Non-Linear Inequalities Nicolas Delanoue, Luc Jaulin, and Bertrand Cottenceau 381 - 398 Optimal Multiplication of G-intervals Lubomir V. Kolev 399 - 408 On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis Sebastien Lagrange, Nicolas Delanoue, and Luc Jaulin 409 - 421

An Application of Interval Methods to Stock Market Forecasting Chenyi Hu and Ling T. He 423 - 434

Interval-Related Talks at the 2007 IEEE Symposium Series on Computational Intelligence 435 - 440 Interval-Related Talks at the North American Fuzzy Information Processing Society Annual Conference NAFIPS'07 441 - 443Back to the Table of Contents of "Reliable Computing"

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Determining the Positive Definiteness Margin of Interval Matrices Lubomir V. Kolev 445 - 466 Computing Population Variance and Entropy under Interval Uncertainty: Linear-Time Algorithms Gang Xiang, Martine Ceberio, and Vladik Kreinovich 467 - 488 Computing the Pessimism of Inclusion Functions Gilles Chabert and Luc Jaulin 489 - 504Back to the Table of Contents of "Reliable Computing"

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