Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces
Bravo
M
author
Cominetti
R
author
Pavez-Signe
M
author
2019
English
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.
Nonexpansive maps
Fixed point iterations
Rates of convergence
Evolution equations
WOS:000465626900008
exported from refbase (http://ficpubs.uai.cl/show.php?record=997), last updated on Thu, 02 Jan 2020 17:47:29 +0000
text
http://ficpubs.uai.cl/files/997_Bravo_etal2019.pdf
10.1007/s10107-018-1240-1
Bravo_etal2019
Mathematical Programming
Math. Program.
2019
Springer Heidelberg
continuing
periodical
academic journal
175
1-2
241
262
0025-5610