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Author Bravo, M.; Cominetti, R.; Pavez-Signe, M.
Title Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces Type
Year 2019 Publication Mathematical Programming Abbreviated Journal Math. Program.
Volume 175 Issue 1-2 Pages 241-262
Keywords Nonexpansive maps; Fixed point iterations; Rates of convergence; Evolution equations
Abstract We study the convergence of an inexact version of the classical Krasnosel'skii-Mann iteration for computing fixed points of nonexpansive maps. Our main result establishes a new metric bound for the fixed-point residuals, from which we derive their rate of convergence as well as the convergence of the iterates towards a fixed point. The results are applied to three variants of the basic iteration: infeasible iterations with approximate projections, the Ishikawa iteration, and diagonal Krasnosels'kii-Mann schemes. The results are also extended to continuous time in order to study the asymptotics of nonautonomous evolution equations governed by nonexpansive operators.
Address [Bravo, Mario] Univ Santiago Chile, Dept Matemat & Ciencia Comp, Alameda Libertador Bernardo Ohiggins 3363, Santiago, Chile, Email: mario.bravo.g@usach.cl;
Corporate Author Thesis
Publisher Springer Heidelberg Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title (up) Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0025-5610 ISBN Medium
Area Expedition Conference
Notes WOS:000465626900008 Approved
Call Number UAI @ eduardo.moreno @ Serial 997
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