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  • Book
  • © 1993

Numerical Toolbox for Verified Computing I

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

Authors:

  1. Ulrich Kulisch

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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  2. Rolf Hammer

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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  3. Dietmar Ratz

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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  4. Matthias Hocks

    1. Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xv
    PDF

  2. Introduction

    1. Introduction

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 1-14

  3. Preliminaries

    1. Front Matter

      Pages 15-15
      PDF

    2. The Features of PASCAL-XSC

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 17-30

    3. Mathematical Preliminaries

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 31-53

  4. One-Dimensional Problems

    1. Front Matter

      Pages 55-55
      PDF

    2. Evaluation of Polynomials

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 57-68

    3. Automatic Differentiation

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 69-86

    4. Nonlinear Equations in One Variable

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 87-104

    5. Global Optimization

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 105-130

    6. Evaluation of Arithmetic Expressions

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 131-151

    7. Zeros of Complex Polynomials

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 152-172

  5. Multi-Dimensional Problems

    1. Front Matter

      Pages 173-173
      PDF

    2. Linear Systems of Equations

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 175-194

    3. Linear Optimization

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 195-224

    4. Automatic Differentiation for Gradients, Jacobians, and Hessians

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 225-263

    5. Nonlinear Systems of Equations

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 264-281

    6. Global Optimization

      • Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks
      Pages 282-311

  6. Back Matter

    Pages 313-339
    PDF
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About this book

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.
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Keywords

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Authors and Affiliations

  • Institut für Angewandte Mathematik, Universität Karlsruhe, Karlsruhe, Germany

    Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks

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Bibliographic Information

  • Book Title: Numerical Toolbox for Verified Computing I

  • Book Subtitle: Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs

  • Authors: Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks

  • Series Title: Springer Series in Computational Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-78423-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-642-78425-5Published: 08 December 2011

  • eBook ISBN: 978-3-642-78423-1Published: 06 December 2012

  • Series ISSN: 0179-3632

  • Series E-ISSN: 2198-3712

  • Edition Number: 1

  • Number of Pages: XV, 339

  • Topics: Numerical Analysis, Programming Techniques

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Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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