Andrzej Cegielski

Iterative Methods for Fixed Point Problems in Hilbert Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 298
• Erscheinungstermin: 14. September 2012
• Englisch
• ISBN-13: 9783642309014
• Artikelnr.: 43791074

Inhaltsangabe

1 Introduction.- 2 Algorithmic Operators.- 3 Convergence of Iterative Methods.- 4 Algorithmic Projection Operators.- 5 Projection methods.

Rezensionen

From the reviews: "This book is mainly concerned with iterative methods to obtain fixed points. ... this book is an excellent introduction to various aspects of the iterative approximation of fixed points of nonexpansive operators in Hilbert spaces, with focus on their important applications to convex optimization problems. It would be an excellent text for graduate students, and, by the way the material is structured and presented, it will also serve as a useful introductory text for young researchers in this field." (Vasile Berinde, Zentralblatt MATH, Vol. 1256, 2013)