Scientific Computation with Automatic Result Verification

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.

Contenu

Automatic Result Verification.- I. Numerical Methods with Result Verification.- A Method for Producing Verified Results for Two-point Boundary Value Problems.- A Kind of Difference Method for Enclosing Solutions of Ordinary Linear Boundary Value Problems.- A Self-validating Method for Solving Linear Programming Problems with Interval Input Data.- Enclosing the Solutions of Linear Equations by Interval Iterative Processes.- Errorbounds for Quadratic Systems of Nonlinear Equations Using the Precise Scalar Product.- Inclusion of Eigenvalues of General Eigenvalue Problems of Matrices.- Verified Inclusion for Eigenvalues of Certain Difference and Differential Equations.- II. Applications in the Technical Sciences.- VIB - Verified Inclusions of Critical Bending Vibrations.- Stability Test for Periodic Differential Equations on Digital Computers with Applications.- The Periodic Solutions of the Oregonator and Verification of Results.- On Arithmetical Problems of Geometric Algorithms in the Plane.- III. Improving the Tools.- Precise Evaluation of Polynomials in Several Variables.- Evaluation of Arithmetic Expressions with Guaranteed High Accuracy.- Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy.- Inverse Standard Functions for Real and Complex Point and Interval Arguments with Dynamic Accuracy.- Inclusion Algorithms with Functions as Data.- FORTRAN-SC. A Study of a FORTRAN Extension for Engineering/Scientific Computation with Access to ACRITH.