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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Yes, you can access Self-Validating Numerics for Function Space Problems by Edgar W. Kaucher,Willard L. Miranker, Werner Rheinboldt in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Academic Press

Year

2014

ISBN

9781483273778

Topic

Mathematics

Subtopic

Mathematical Analysis

Index

Mathematics

Front Cover
Self-Validating Numerics for Function Space Problems
Copyright Page
Table of Contents
Dedication
Preface
Acknowledgments
Chapter 1. Introduction
Chapter 2. Mathematical Preliminaries
Chapter 3. Ultra-arithmetic and Roundings
Chapter 4. Methods for Functional Equations
Chapter 5. Iterative Residual Correction
Chapter 6. Comments on Programming Language
Chapter 7. Application and Illustrative Computation
Glossaries
References