Hans J. Stetter

In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, Numerical Polynomial Algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas.

Numerical Polynomial Algebra

Ulrich Kulisch

Scientific Computation with Result Verification has been a persevering research topic at the Institute for Applied Mathematics of Karlsruhe University for many years. A good number of meetings have been devoted to this area. The latest of these meetings was held from 30 September to 2 October, 1987, in Karlsruhe; it was co-sponsored by the GAMM Committee on "Computer Arithmetic and Scientific Computation". - - This volume combines edited versions of selected papers presented at this confer ence, including a few which were presented at a similar meeting one year earlier. The selection was made on the basis of relevance to the topic chosen for this volume. All papers are original contributions. In an appendix, we have supplied a short account of the Fortran-SC language which permits the programming of algorithms with result verification in a natural manner. The editors hope that the publication of this material as a Supplementum of Computing will further stimulate the interest of the scientific community in this important tool for Scientific Computation. In particular, we would like to make application scientists aware of its potential. The papers in the second chapter of this volume should convince them that automatic result verification may help them to design more reliable software for their particular tasks. We wish to thank all contributors for adapting their manuscripts to the goals of this volume. We are also grateful to the Publisher, Springer-Verlag of Vienna, for an efficient and quick production.

Hans J. Stetter

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