Computer Arithmetic and Self-Validating Numerical Methods

Computer Arithmetic and Self-Validating Numerical Methods

1st Edition - August 28, 1990

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  • Editor: Christian Ullrich
  • eBook ISBN: 9781483267814

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Description

Notes and Reports in Mathematics in Science and Engineering, Volume VII: Computer Arithmetic and Self-Validating Numerical Methods compiles papers presented at the first international conference on “Computer Arithmetic and Self-Validating Numerical Methods,” held in Basel from October 2 to 6, 1989. This book begins by providing a tutorial introduction to computer arithmetic with operations of maximum accuracy, differentiation arithmetic and enclosure methods, and programming languages for self-validating numerical methods. The rest of the chapters discuss the determination of guaranteed bounds for eigenvalues by variational methods and guaranteed inclusion of solutions of differential equations. An appendix covering the IMACS-GAMM resolution on computer arithmetic is provided at the end of this publication. This volume is recommended for researchers and professionals working on computer arithmetic and self-validating numerical methods.

Table of Contents


  • Contributors

    Preface

    Acknowledgments

    What Do We Need beyond IEEE Arithmetic?

    Chips for High Precision Arithmetic

    Enclosure Methods

    Differentiation Arithmetics

    Industrial Applications of Interval Techniques

    Programming Languages for Enclosure Methods

    The Determination of Guaranteed Bounds to Eigenvalues with the Use of Variational Methods I

    The Determination of Guaranteed Bounds to Eignevalues with the Use of Variational Methods II

    Validated Solution of Initial Value Problems for ODE

    Guaranteed Inclusions of Solutions of Some Types of Boundary Value Problems

    Periodic Solutions: Enclosure, Verification, and Applications

    Numerical Algorithms for Existence Proofs and Error Estimates for Two-Point Boundary Value Problems

    Aspects of Self-Validating Numerics in Banach Spaces

    Appendix: IMACS-GAMM Resolution on Computer Arithmetic

Product details

  • No. of pages: 316
  • Language: English
  • Copyright: © Academic Press 1990
  • Published: August 28, 1990
  • Imprint: Academic Press
  • eBook ISBN: 9781483267814

About the Editor

Christian Ullrich

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