Special Issue of Journal of Symbolic Computation

on Symbolic-Numeric Algebra for Polynomials

In such situations, the usual concepts and algorithms of computer algebra are not immediately applicable. Appropriate approaches must utilize ideas and algorithmic techniques from numeric computation together with standard and possibly extended procedures from classical computer algebra. The emerging area of mathematics dealing with this situation may be thought of as "numerical nonlinear algebra", in analogy with the well-known area of "numerical linear algebra".

While some work in this field had already begun in the 1980s, activities have recently been growing in depth and breadth. This summer the workshop SNAP 96, held at INRIA Sophia Antipolis (France), brought a focus to the area of symbolic-numeric algebra for polynomials. The literature in this area has appeared in various locations, but has until now been quite dispersed and difficult to locate. It appears timely to collect some outstanding results of this development into a special issue of the Journal of Symbolic Computation.

We invite submissions for this special issue on Symbolic-Numeric Algebra for Polynomials. Such papers should contribute to the understanding of the inter- action of symbolic and numeric computing. Their results should be relevant for the design of algorithms for the solution of related problems and the computer implementation of such algorithms. Relevant topics include, but are not restricted to:

- GCD computation for polynomials with inexactly-known coefficients;
- symbolic-numeric methods for simplifying and solving multivariate polynomial systems;
- matrix methods oriented towards zero-dimensional ideals (e.g. multivariate resultants);
- methods for other approximate polynomial problems (e.g. factorization, Pade approximation);
- software systems for the efficient implementation of such algorithms, taking advantage of existing numerical libraries.

Deadline for submission of full papers: 31 March, 1997

Notification of acceptance/rejection: 30 June, 1997

Final revised manuscripts due: 30 September, 1997

Appearance of special issue: early in 1998

Guest editors:

Stephen Watt

IBM T.J. Watson Research Center

P.O.Box 218, Yorktown Heights NY 10598 USA

smwatt@watson.ibm.com

Hans J. Stetter

Technical University

A-1040 Vienna, Austria

stetter@uranus.tuwien.ac.at

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