Interval analysis : and automatic result verification / Günter Mayer.

Format:

Book

Author/Creator:

Mayer, Günter, author.

Series:

De Gruyter studies in mathematics ; Volume 65.

De Gruyter Studies in Mathematics, 0179-0986 ; Volume 65

Language:

English

Subjects (All):

Interval analysis (Mathematics).

Physical Description:

1 online resource (518 pages).

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2017.

Language Note:

In English.

Summary:

This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals

Contents:

Frontmatter

Preface

Contents

1. Preliminaries

2. Real intervals

3. Interval vectors, interval matrices

4. Expressions, P-contraction, ε-inflation

5. Linear systems of equations

6. Nonlinear systems of equations

7. Eigenvalue problems and related ones

8. Automatic differentiation

9. Complex intervals

Final Remarks

Appendix

A. Proof of the Jordan normal form

B. Two elementary proofs of Brouwer's fixed point theorem

C. Proof of the Newton-Kantorovich Theorem

D. Convergence proof of the row cyclic Jacobi method

E. The CORDIC algorithm

F. The symmetric solution set - a proof of Theorem 5.2.6

G. A short introduction to INTLAB

Bibliography

Symbol Index

Author Index

Subject Index

Notes:

Includes bibliographical references and indexes.

Description based on online resource; title from PDF title page (ebrary, viewed May 4, 2017).

ISBN:

9783110498059

3110498057

9783110499469

3110499460

OCLC:

984647843