β Scribed by Kaucher, Edgar W.; Miranker, Willard L
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Self-Validating Numerics for Function Space Problems.
Content: Front Cover
Self-Validating Numerics for Function Space Problems
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgments
Chapter1. Introduction
E-Methods
Ultra-arithmetic
Computer Arithmetic
Suggestions to the Reader
Chapter 2. Mathematical Preliminaries
2.1 Basic Formulation of Self-Validating Methods in M
2.2 A Broader Setting for Self-Validating Methods
Chapter 3. Ultra-arithmetic and Roundings
3.1 Spaces, Bases, Roundings, and Approximate Operations
3.2 Spaces, Bases, and Roundings for Validation
Chapter 4. Methods for Functional Equations. 4.1 Methods for Linear Equations4.2 Methods for Nonlinear Function Equations
Chapter 5. Iterative Residual Correction
5.1 Arithmetic Implications of IRC
5.2 IRC for Initial-Value Problems and Volterra Integral Equations
5.3 Iterative Residual Correction with Carry
5.4 A Formalism for IRC in Function Space
Chapter 6. Comments on Programming Language
Chapter 7. Application and Illustrative Computation
7.1 Review of the Computational Process
7.2 Illustrative Computation
Glossaries
References.
Function spaces;Numerical analysis;MATHEMATICS -- Calculus;MATHEMATICS -- Mathematical Analysis
π SIMILAR VOLUMES
This monograph is a cumulation mainly of the author's research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is the illustration of almost
<p>Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applica
This monograph is a cumulation mainly of the author's research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is the illustration of almost