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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 Journal Article
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 Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0025-5610 ISBN Medium
Area Expedition Conference
Notes WOS:000465626900008 Approved no
Call Number UAI @ eduardo.moreno @ Serial 997
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