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Scientific Computation with Automatic Result Verification

  • Conference proceedings
  • © 1988

Overview

Editors:
  1. Ulrich Kulisch

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Federal Republic of Germany

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  2. Hans J. Stetter

    1. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Austria

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Computing Supplementa (COMPUTING, volume 6)

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Table of contents (18 papers)

  1. Front Matter

    Pages I-VIII
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  2. Automatic Result Verification

    1. Automatic Result Verification

      • U. Kulisch, H. J. Stetter
      Pages 1-6

  3. Numerical Methods with Result Verification

    1. Front Matter

      Pages 7-7
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    2. A Method for Producing Verified Results for Two-Point Boundary Value Problems

      • Johann Schröder
      Pages 9-22

    3. A Kind of Difference Methods for Enclosing Solutions of Ordinary Linear Boundary Value Problems

      • Johannes Weissinger
      Pages 23-31

    4. A Self-Validating Method for Solving Linear Programming Problems with Interval Input Data

      • Christian Jansson
      Pages 33-45

    5. Enclosing the Solutions of Systems of Linear Equations by Interval Iterative Processes

      • Günter Mayer
      Pages 47-58

    6. Errorbounds for Quadratic Systems of Nonlinear Equations Using the Precise Scalar Product

      • G. Alefeld
      Pages 59-67

    7. Inclusion of Eigenvalues of General Eigenvalue Problems for Matrices

      • Henning Behnke
      Pages 69-78

    8. Verified Inclusion for Eigenvalues of Certain Difference and Differential Equations

      • Martin Ohsmann
      Pages 79-87

  4. Applications in the Technical Sciences

    1. Front Matter

      Pages 89-89
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    2. VIB — Verified Inclusions of Critical Bending Vibrations

      • A. Ams, W. Klein
      Pages 91-98

    3. Stability Test for Periodic Differential Equations on Digital Computers with Applications

      • Dietrich Cordes
      Pages 99-110

    4. The Periodic Solutions of the Oregonator and Verification of Results

      • E. Adams, A. Holzmüller, D. Straub
      Pages 111-121

    5. On Arithmetical Problems of Geometric Algorithms in the Plane

      • Th. Ottmann, G. Thiemt, Ch. Ullrich
      Pages 123-136
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About this book

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.

Editors and Affiliations

  • Institut für Angewandte Mathematik, Universität Karlsruhe, Federal Republic of Germany

    Ulrich Kulisch

  • Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Austria

    Hans J. Stetter

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