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Author (up) Bravo, M.; Cominetti, R.; Pavez-Signe, M. doi  openurl
  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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