Computer Arithmetic and Self-Validating Numerical Methods - 1st Edition - ISBN: 9780127082455, 9781483267814

Computer Arithmetic and Self-Validating Numerical Methods

1st Edition

Editors: Christian Ullrich
eBook ISBN: 9781483267814
Imprint: Academic Press
Published Date: 28th August 1990
Page Count: 316
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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




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


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© Academic Press 1990
Academic Press
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About the Editor

Christian Ullrich

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