Self-validating numerics for function space problems: Computation with guarantees for differential and integral equations (Notes and reports in computer science and applied mathematics) - Hardcover

Kaucher, Edgar W. & Willard L. Miranker.

Hardcover

ISBN 10: 0124020208 ISBN 13: 9780124020207

Publisher: Academic Press, Inc., 1984

Synopsis

Self-Validating Numerics for Function Space Problems describes the development of computational methods for solving function space problems, including differential, integral, and function equations. This seven-chapter text highlights three approaches, namely, the E-methods, ultra-arithmetic, and computer arithmetic.After a brief overview of the different self-validating approaches, this book goes on introducing the mathematical preliminaries consisting principally of fixed-point theorems and the computational context for the development of validating methods in function spaces. The subsequent chapters deals with the development and application of point of view of ultra-arithmetic and the constructs of function-space arithmetic spaces, such as spaces, bases, rounding, and approximate operations. These topics are followed by discussion of the iterative residual correction methods for function problems and the requirements of a programming language needed to make the tools and constructs of the methodology available in actual practice on a computer. The last chapter describes the techniques for adapting the methodologies to a computer, including the self-validating results for specific problems.This book will prove useful to mathematicians and advance mathematics students.

Edition details

• Publisher: Academic Press, Inc.
• Publication date: 1984
• Language: English
• ISBN 10: 0124020208
• ISBN 13: 9780124020207
• Binding: Hardcover
• Edition number: 1
• Number of pages: 255