Iterative Methods for Fixed Point Problems in Hilbert Spaces

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Applied
Cover of the book Iterative Methods for Fixed Point Problems in Hilbert Spaces by Andrzej Cegielski, Springer Berlin Heidelberg
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Author: Andrzej Cegielski ISBN: 9783642309014
Publisher: Springer Berlin Heidelberg Publication: September 14, 2012
Imprint: Springer Language: English
Author: Andrzej Cegielski
ISBN: 9783642309014
Publisher: Springer Berlin Heidelberg
Publication: September 14, 2012
Imprint: Springer
Language: English

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.

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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.

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