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Title
Approximate solutions of common fixed-point problems [electronic resource] / Alexander J. Zaslavski.
ISBN
9783319332550 (electronic book)
3319332554 (electronic book)
9783319332536
3319332538
Published
Switzerland : Springer, 2016.
Language
English
Description
1 online resource (ix, 454 pages).
Item Number
10.1007/978-3-319-33255-0 doi
Call Number
QA329.9
Dewey Decimal Classification
515/.7248
Summary
This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal algorithm · common fixed point problems in metric spaces · common fixed point problems in the spaces with distances of the Bregman type · a proximal algorithm for finding a common zero of a family of maximal monotone operators · subgradient projections algorithms for convex feasibility problems in Hilbert spaces .
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 11, 2016).
Series
Springer optimization and its applications ; v. 112.
Available in Other Form
Print version: 9783319332536
1.Introduction
2. Dynamic string-averaging methods in Hilbert spaces
3. Iterative methods in metric spaces
4. Dynamic string-averaging methods in normed spaces
5. Dynamic string-maximum methods in metric spaces
6. Spaces with generalized distances
7. Abstract version of CARP algorithm
8. Proximal point algorithm
9. Dynamic string-averaging proximal point algorithm
10. Convex feasibility problems
11. Iterative subgradient projection algorithm
12. Dynamic string-averaging subgradient projection algorithm.- References.- Index. .
