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Self-Validating Numerics for Function Space Problems : Computation with Guarantees for Differential and Integral Equations - Edgar W. Kaucher

Self-Validating Numerics for Function Space Problems

Computation with Guarantees for Differential and Integral Equations

By: Edgar W. Kaucher, Willard L. Miranker

eText | 20 June 2014 | Edition Number 1

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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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