Franklin

Iterative Approximation of Fixed Points [electronic resource] / by Vasile Berinde.

Author/Creator:
Berinde, Vasile. author., Author,
Publication:
Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
Format/Description:
Book
1 online resource (XV, 326 pages)
Series:
Lecture Notes in Mathematics, 0075-8434 ; 1912
Lecture Notes in Mathematics, 0075-8434 ; 1912
Contained In:
Springer eBooks
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Subjects:
Operator theory.
Numerical analysis.
Topology.
Local subjects:
Operator Theory. (search)
Numerical Analysis. (search)
Topology. (search)
System Details:
text file PDF
Summary:
The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration et cetera), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.
Contents:
Pre-Requisites of Fixed Points
The Picard Iteration
The Krasnoselskij Iteration
The Mann Iteration
The Ishikawa Iteration
Other Fixed Point Iteration Procedures
Stability of Fixed Point Iteration Procedures
Iterative Solution of Nonlinear Operator Equations
Error Analysis of Fixed Point Iteration Procedures.
Contributor:
SpringerLink (Online service)
Other format:
Printed edition:
Printed edition:
ISBN:
9783540722342
Publisher Number:
10.1007/978-3-540-72234-2 doi
Access Restriction:
Restricted for use by site license.