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Iterative Methods for Fixed Point Problems in Hilbert Spaces [electronic resource] / by Andrzej Cegielski.

By: Cegielski, Andrzej [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 2057Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013Description: XVI, 298 p. 61 illus., 3 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642309014.Subject(s): Mathematics | Functional analysis | Operator theory | Numerical analysis | Mathematical optimization | Mathematics | Optimization | Functional Analysis | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Operator TheoryDDC classification: 519.6 Online resources: Click here to access online
Contents:
1 Introduction -- 2 Algorithmic Operators -- 3 Convergence of Iterative Methods -- 4 Algorithmic Projection Operators -- 5 Projection methods.
In: Springer eBooksSummary: 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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1 Introduction -- 2 Algorithmic Operators -- 3 Convergence of Iterative Methods -- 4 Algorithmic Projection Operators -- 5 Projection methods.

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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