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Author |
Bravo, M.; Cominetti, R.; Pavez-Signe, M. |
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Title |
Rates of convergence for inexact Krasnosel'skii-Mann iterations in Banach spaces |
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Year |
2019 |
Publication |
Mathematical Programming |
Abbreviated Journal |
Math. Program. |
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Volume |
175 |
Issue |
1-2 |
Pages |
241-262 |
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Keywords |
Nonexpansive maps; Fixed point iterations; Rates of convergence; Evolution equations |
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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. |
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Address |
[Bravo, Mario] Univ Santiago Chile, Dept Matemat & Ciencia Comp, Alameda Libertador Bernardo Ohiggins 3363, Santiago, Chile, Email: mario.bravo.g@usach.cl; |
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Publisher |
Springer Heidelberg |
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Language |
English |
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ISSN |
0025-5610 |
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Notes |
WOS:000465626900008 |
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Call Number |
UAI @ eduardo.moreno @ |
Serial |
997 |
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