Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces

• 成果类型: Article
• 署名作者: Bravo, Mario; Cominetti, Roberto; Pavez-Signe, Matias
• 署名单位: Universidad de Santiago de Chile; Universidad Adolfo Ibanez; Universidad de Chile
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1240-1
• 发表日期: 2019
• 页码: 241-262

摘要

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.