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Numerical Toolbox for Verified Computing I

Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs

  • Ulrich Kulisch
  • Rolf Hammer
  • Dietmar Ratz
  • Matthias Hocks

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 21)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Introduction

    1. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 1-14
  3. Preliminaries

    1. Front Matter
      Pages 15-15
    2. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 17-30
    3. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 31-53
  4. One-Dimensional Problems

    1. Front Matter
      Pages 55-55
    2. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 57-68
    3. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 69-86
    4. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 87-104
    5. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 105-130
    6. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 131-151
    7. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 152-172
  5. Multi-Dimensional Problems

    1. Front Matter
      Pages 173-173
    2. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 175-194
    3. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 195-224
    4. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 225-263
    5. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 264-281
    6. Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 282-311
  6. Back Matter
    Pages 313-339

About this book

Introduction

As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns for a given problem. All algorithms we present are influenced by this central concern. We must point out that there is no relationship between our methods of numerical result verification and the methods of program verification to prove the correctness of an imple~entation for a given algorithm. This book is the first to offer a general discussion on • arithmetic and computational reliability, • analytical mathematics and verification techniques, • algorithms, and • (most importantly) actual implementations in the form of working computer routines. Our task has been to find the right balance among these ingredients for each topic. For some topics, we have placed a little more emphasis on the algorithms. For other topics, where the mathematical prerequisites are universally held, we have tended towards more in-depth discussion of the nature of the computational algorithms, or towards practical questions of implementation. For all topics, we present exam­ ples, exercises, and numerical results demonstrating the application of the routines presented.

Keywords

PASCAL-XSC Vereinfachung der Programmierung Verified Computing algorithms automatische Ergebnisveriifikation numerical analysis numerics optimization program verification programming scientific computing selbstverifizierende Numerik simplification simplification of programming verification

Authors and affiliations

  • Ulrich Kulisch
    • 1
  • Rolf Hammer
    • 1
  • Dietmar Ratz
    • 1
  • Matthias Hocks
    • 1
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-78423-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-78425-5
  • Online ISBN 978-3-642-78423-1
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site