| Record |
| Author |
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 |
| Permanent link to this record |
