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Validation Numerics

Theory and Applications

  • Book
  • © 1993

Overview

Editors:
  1. R. Albrecht

    1. Institut für Informatik, Universität Innsbruck, Austria

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  2. G. Alefeld

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

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    You can also search for this editor in PubMed   Google Scholar

  3. H. 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 9)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-ix
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  2. On a Unified Concept of Mathematics

    • N. Apostolatos
    Pages 1-10

  3. A General Approach to a Class of Single-Step Methods for the Simultaneous Inclusion of Polynomial Zeros

    • L. Atanassova, J. Herzberger
    Pages 11-19

  4. On Some Properties of an Interval Newton Type Method and its Modification

    • N. S. Dimitrova
    Pages 21-32

  5. Verified Solution of the Integral Equations for the Two-Dimensional Dirichlet and Neumann Problem

    • Hans-Jürgen Dobner
    Pages 33-43

  6. Two-Stage Interval Iterative Methods

    • A. Frommer, G. Mayer
    Pages 45-65

  7. Convergence Acceleration for Some Rootfinding Methods

    • Weimin Han, F. A. Potra
    Pages 67-78

  8. A Program for Enclosing Cumulative Binomial Probabilities

    • G. Heindl
    Pages 79-92

  9. Effective Evaluation of Hausdorff Distances for Finite Unions of Hyperrectangles

    • K.-U Jahn
    Pages 93-100

  10. A Verified Computation of Fourier-Representations of Solutions for Functional Equations

    • E. Kaucher, Ch. Baumhof
    Pages 101-115

  11. The Cluster Problem in Global Optimization: the Univariate Case

    • B. Kearfott, K. Du
    Pages 117-127

  12. Developing Expert Systems for Validating Numerics

    • S. König, C. P. Ullrich
    Pages 129-146

  13. Computation of Interval Bounds for Weierstrass’ Elliptic Function ℘(z)

    • Walter Krämer, Bertram Barth
    Pages 147-159

  14. Solving Nonlinear Elliptic Problems with Result Verification Using an H -1 Type Residual Iteration

    • Mitsuhiro T. Nakao
    Pages 161-173

  15. The Wrapping Effect, Ellipsoid Arithmetic, Stability and Confidence Regions

    • A. Neumaier
    Pages 175-190

  16. Validated Solution of Large Linear Systems

    • Siegfried M. Rump
    Pages 191-212

  17. The Interval Buneman Algorithm for Arbitrary Block Dimension

    • H. Schwandt
    Pages 213-231

  18. On the Existence and the Verified Determination of Homoclinic and Heteroclinic Orbits of the Origin for the Lorenz Equations

    • H. Spreuer, E. Adams
    Pages 233-246

  19. Verification in Computer Algebra Systems

    • H. J. Stetter
    Pages 247-263

  20. FORTRAN-XSC A Portable Fortran 90 Module Library for Accurate and Reliable Scientific Computing

    • W. V. Walter
    Pages 265-285
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Keywords

About this book

The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.

Editors and Affiliations

  • Institut für Informatik, Universität Innsbruck, Austria

    R. Albrecht

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

    G. Alefeld

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

    H. J. Stetter

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