Self-Validating Numerics for Function Space Problems: Computation with Guarantees for Differential and Integral Equations - Softcover

Kaucher, Edgar W.

9781483241449: Self-Validating Numerics for Function Space Problems: Computation with Guarantees for Differential and Integral Equations

Softcover

ISBN 10: 1483241440 ISBN 13: 9781483241449

Publisher: Academic Press, 2014

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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.

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