Iterative Methods for Fixed Point Problems in Hilbert Spaces

✍ Scribed by Andrzej Cegielski (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2013
• Tongue: English
• Leaves: 315
• Series: Lecture Notes in Mathematics 2057
• Edition: 1
• Category: Library

✦ Synopsis

Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.

✦ Table of Contents

Front Matter....Pages i-xvi
Introduction....Pages 1-38
Algorithmic Operators....Pages 39-103
Convergence of Iterative Methods....Pages 105-127
Algorithmic Projection Operators....Pages 129-202
Projection Methods....Pages 203-274
Back Matter....Pages 275-298

✦ Subjects

Optimization; Functional Analysis; Calculus of Variations and Optimal Control; Optimization; Numerical Analysis; Operator Theory