eBook - PDF
Self-Validating Numerics for Function Space Problems
Computation with Guarantees for Differential and Integral Equations
- 270 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Self-Validating Numerics for Function Space Problems
Computation with Guarantees for Differential and Integral Equations
About this book
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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Information
Table of contents
- 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
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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 & Calculus. We have over one million books available in our catalogue for you to explore.