Functional Analysis and Numerical Mathematics

Lothar Collatz

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483264004
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Functional Analysis and Numerical Mathematics focuses on the structural changes which numerical analysis has undergone, including iterative methods, vectors, integral equations, matrices, and boundary value problems. The publication first examines the foundations of functional analysis and applications, including various types of spaces, convergence and completeness, operators in Hilbert spaces, vector and matrix norms, eigenvalue problems, and operators in pseudometric and other special spaces. The text then elaborates on iterative methods. Topics include the fixed-point theorem for a general iterative method in pseudometric spaces; special cases of the fixed-point theorem and change of operator; iterative methods for differential and integral equations; and systems of equations and difference methods. The manuscript takes a look at monotonicity, inequalities, and other topics, including monotone operators, applications of Schauder's theorem, matrices and boundary value problems of monotone kind, discrete Chebyshev approximation and exchange methods, and approximation of functions. The publication is a valuable source of data for mathematicians and researchers interested in functional analysis and numerical mathematics.

Table of contents

• Front Cover
• Functional Analysis and Numerical Mathematics
• Copyright Page
• Table of Contents
• Translator's Note
• Preface to the German Edition
• Notation
• CHAPTER I. Foundations of Functional Analysis and Applications
• CHAPTER II. Iterative Methods
• CHAPTER III. Monotonicity, Inequalities, and Other Topics
• APPENDIX
• Remarks on Schauder's Fixed-Point Theorem
• REFERENCES
• Author Index
• Subject Index