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Approximate Solutions of Common Fixed-Point Problems

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Approximate Solutions of Common Fixed-Point Problems/ by Alexander J. Zaslavski.
作者:	Zaslavski, Alexander J.
面頁冊數:	IX, 454 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Calculus of variations. -
電子資源:	https://doi.org/10.1007/978-3-319-33255-0
ISBN:	9783319332550

Approximate Solutions of Common Fixed-Point Problems
Zaslavski, Alexander J.

Approximate Solutions of Common Fixed-Point Problems[electronic resource] /by Alexander J. Zaslavski. - 1st ed. 2016. - IX, 454 p.online resource. - Springer Optimization and Its Applications,1121931-6828 ;. - Springer Optimization and Its Applications,104.

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. .

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 .

ISBN: 9783319332550

Standard No.: 10.1007/978-3-319-33255-0doiSubjects--Topical Terms:

527927
Calculus of variations.

LC Class. No.: QA315-316

Dewey Class. No.: 515.64

Approximate Solutions of Common Fixed-Point Problems
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520 $a 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 .
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