Scientific Computing, Validated Numerics, Interval Methods

edited by:
Walter Kraemer (University of Wuppertal, Germany)
and Juergen Wolff v. Gudenberg (University of Wuerzburg, Germany)

Kluwer Academic Publishers, Boston/Dordrecht/London, 2001


Preface                                                  xi

SCAN 2000 Keynote Address The Future of Intervals         1
G. William Walster

Part I. Software and Hardware Tools

Variable-Precision Exponential Evaluation       
Javier Hormigo, Julio Villalba, and Michael J. Schulte   19

Fast computation of some special integrals of 
mathematical physics      
Ekatherina A. Karatsuba                                  29

Interval Input and Output       
Eero Hyvoenen                                            41

A Case for Interval Hardware on Superscalar Processors  
James E. Stine and Michael J. Schulte                    53

Evaluating the Impact of Accurate Branch Prediction 
on Interval Software        
Ahmet Akkas, Michael J. Schulte, and James E. Stine      69

Automatic Test Case Generation using Interval 
Guenter Schumacher and Armin Bantle                      81

Part II. Linear Algebra

On the Hull of the Solution Sets of Interval 
Linear Equations   
Jana Konickova                                           91

Computation of Algebraic Solutions to Interval 
Systems via Systems of Coordinates       
Svetoslav Markov                                        103

Towards Diagrammatic Analysis of Systems of 
Interval "Linear Equations" 
Zenon Kulpa                                             115

On the Solution of Parametrised Linear Systems  
Evgenija D. Popova                                      127

Part III. Polynomials

Verified Solutions of Systems of Nonlinear 
Polynomial Equations 141
Daniela Fausten and Wolfram Luther                      141

Euler-Like Method with Weierstrass' Correction   
Miodrag S. Petkovic and Dejan V. Vranic                 153

Part IV. Set Enclosures

Guaranteed Set Computation with Subpavings      
Michel Kieffer, Isabelle Braems, Eric Walter, 
and Luc Jaulin                                          167

A New Intersection Algorithm for Parametric 
Surfaces Based on LIEs      
Katja Buehler and Wilhelm Barth                         179

State Estimation Using Interval Constraint Propagation  
Luc Jaulin, Isabelle Braems, Michel Kieffer,
and Eric Walter                                         191

Part V. Global Optimization

Interval Methods for Global Optimization Using 
the Boxing Method        
Andras Erik Csallner, Rudi Klatte, Dietmar Ratz, 
and Andreas Wiethoff                                    205

A Branch-and-Prune Method for Global Optimization       
Dimitris G. Sotiropoulos and Theodoula N. Grapsa        215

Simulation of a Controlled Aircraft Elevator 
under Sensor Uncertainties 
Juergen Heeks, Eberhard P. Hofer, Bernd Tibken, 
Karin Lunde, and Klaus Thorwart                         227

Part VI. Control

Traditional Parameter Estimation Versus Estimation 
of Guaranteed Parameter Sets 
Eberhard P. Hofer, Bernd Tibken, and Milan Vlach        241

Stabilizing Control Design of Nonlinear Process 
Involving Uncertainties 
Mikhail Krastanov and Neli Dimitrova                    255

Set Estimation, Computation of Volumes and Data Safety  
Isabelle Braems, Michel Kieffer, Eric Walter, 
and Luc Jaulin                                          267

Part VII. ODE and DAE and Applications

Verified High-Order Integration of DAEs and 
Higher-Order ODEs   
Jens Hoefkens, Martin Berz, and Kyoko Makino            281

About a Finite Dimensional Reduction Method for 
Conservative Dynamical Systems and its Applications     
Anatoliy Prykarpatsky, Stanislaw Brzychczy, 
and V. Samoylenko                                       293

Verified Determination of Singularities in Chemical 
Christian H. Bischof, Bruno Lang, 
Wolfgang Marquardt, and Martin Moennigmann              305

Modeling of Multibody Systems with Interval Arithmetic  
Christian Hoersken and Holger Traczinski                317

Part VIII. Stochastics and Probability

On the Algebraic Properties of Stochastic 
Arithmetic. Comparison to Interval Arithmetic      
Rene Alt and Svetoslav Markov                           331

Global Random Walk Simulations of Diffusion             
Calin Vamos, Nicolae Suciu, Harry Vereecken, 
Olaf Nitzsche, and Horst Hardelauf                      343

Interval Computations as a Particular Case of a 
General Scheme Involving Classes of Probability 
Scott Ferson, Lev Ginzburg, Vladik Kreinovich, 
and Harry Schulte                                       355

For Reliable and Powerful Scientific Computations       
Fabienne Jezequel and Jean-Marie Chesneaux              367

Reliable Representations of Strange Attractors  
Dominique Michelucci                                    379


The Referees                                            391

[<--] Back to Books on Interval Computations

[<--] Back to the main menu of the Interval Computations website