Solutions of Fixed Point Problems with Computational Errors

Alexander J. Zaslavski

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English

Springer International Publishing AG
20 March 2024

Functional analysis & transforms; Numerical analysis; Optimisation

Series: Springer Optimization and Its Applications

The book is devoted to the study of approximate solutions of fixed point problems in the presence of computational errors. It begins with a study of approximate solutions of star-shaped feasibility problems in the presence of perturbations. The goal is to show the convergence of algorithms, which are known as important tools for solving convex feasibility problems and common fixed point problems.

The text also presents studies of algorithms based on unions of nonexpansive maps, inconsistent convex feasibility problems, and split common fixed point problems. A number of algorithms are considered for solving convex feasibility problems and common fixed point problems. The book will be of interest for researchers and engineers working in optimization, numerical analysis, and fixed point theory. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of the influence of computational errorsfor several important algorithms used for nonconvex feasibility problems.

By: Alexander J. Zaslavski
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2024 ed.
Volume: 210
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031508783
ISBN 10: 3031508785
Series: Springer Optimization and Its Applications
Pages: 386
Publication Date: 20 March 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1 - Introduction.- 2 - Iterative methods in a Hilbert space.- 3 - The Cimmino algorithm in a Hilbert space.- 4 - Dynamic string-averaging methods in Hilbert spaces.- 5 - Methods with remotest set control in a Hilbert space.- 6 - Algorithms based on unions of nonexpansive maps.- 7 - Inconsistent convex feasibility problems.- 8 - Split common fixed point problems.

Alexander J. Zaslavski, Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel.