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Author (up) Bravo, M.; Cominetti, R.
Title Sharp convergence rates for averaged nonexpansive maps Type
Year 2018 Publication Israel Journal Of Mathematics Abbreviated Journal Isr. J. Math.
Volume 227 Issue 1 Pages 163-188
Keywords
Abstract We establish sharp estimates for the convergence rate of the Kranosel'skiA-Mann fixed point iteration in general normed spaces, and we use them to show that the optimal constant of asymptotic regularity is exactly . To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance between the iterates. We show that these bounds are tight by building a nonexpansive map T: [0, 1](N) -> [0, 1](N) that attains them with equality, settling a conjecture by Baillon and Bruck. The recursive bounds are in turn reinterpreted as absorption probabilities for an underlying Markov chain which is used to establish the tightness of the constant 1/root pi.
Address [Bravo, Mario] Univ Santiago Chile, Dept Matemat & Ciencia Computac, Alameda Libertador Bernardo Ohiggins 3363, Santiago, Chile, Email: mario.bravo.g@usach.cl;
Corporate Author Thesis
Publisher Hebrew Univ Magnes Press Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0021-2172 ISBN Medium
Area Expedition Conference
Notes WOS:000442512900006 Approved
Call Number UAI @ eduardo.moreno @ Serial 909
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Author (up) 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 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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