Approximate Solutions of Common Fixed-Point Problems (Springer Optimization and Its Applications #112)

By: Alexander J. Zaslavski

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Synopsis: This book presents results on theconvergence behavior of algorithms which are known as vital tools for solvingconvex feasibility problems and common fixed point problems. The main goal forus in dealing with a known computational error is to find what approximatesolution can be obtained and how many iterates one needs to find it. Accordingto know results, these algorithms should converge to a solution. In thisexposition, these algorithms are studied, taking into account computationalerrors which remain consistent in practice. In this case the convergence to asolution does not take place. We show that our algorithms generate a goodapproximate solution if computational errors are bounded from above by a smallpositive constant. Beginning with an introduction, this monograph moves onto study: · dynamicstring-averaging methods for common fixed point problems in a Hilbert space · dynamicstring methods for common fixed point problems in a metric space · dynamicstring-averaging version of the proximal algorithm · common fixedpoint problems in metric spaces · common fixedpoint problems in the spaces with distances of the Bregman type · a proximalalgorithm for finding a common zero of a family of maximal monotone operators · subgradientprojections algorithms for convex feasibility problems in Hilbert spaces