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Mathematics | Iterative Methods for Fixed Point Problems in Hilbert Spaces

Iterative Methods for Fixed Point Problems in Hilbert Spaces

Series: Lecture Notes in Mathematics, Vol. 2057

Cegielski, Andrzej

2013, XVI, 298 p. 61 illus., 3 illus. in color.

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  • The projection methods for fixed point problems are presented in a consolidated way
  • Over 60 figures help to understand the properties of important classes of algorithmic operators
  • The convergence properties of projection methods follow from a few general convergence theorems presented in the monograph
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.

Content Level » Research

Keywords » 47-02, 49-02, 65-02, 90-02, 47H09, 47J25, 37C25, 65F10 - fixed point - projection methods - quasi-nonexpansive operator

Related subjects » Analysis - Computational Science & Engineering - Mathematics

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