Rate Of Convergence Of Some Space Decomposition Methods For Linear And Nonlinear Problems (1998)
| Venue: | SIAM J. Numer. Anal |
| Citations: | 31 - 14 self |
BibTeX
@ARTICLE{Tai98rateof,
author = {Xue-cheng Tai and Magne Espedal},
title = {Rate Of Convergence Of Some Space Decomposition Methods For Linear And Nonlinear Problems},
journal = {SIAM J. Numer. Anal},
year = {1998},
volume = {35},
pages = {1558--1570}
}
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Abstract
.<F3.784e+05> Convergence of a space decomposition method is proved for a class of convex programming problems. A space decomposition refers to a method that decomposes a space into a sum of subspaces, which could be a domain decomposition or a multilevel method when applied to partial di#erential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems, and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems.<F4.005e+05> Key words.<F3.784e+05> parallel, domain decomposition, nonlinear, elliptic equation, space decomposition<F4.005e+05> AMS subject classifications.<F3.784e+05> 65J10, 65M55, 65Y05<F4.005e+05> PII.<F3.784e+05> S0036142996297461<F4.795e+05> 1. Introduction.<F4.397e+05> We use space decomposition methods to solve a convex programming problem. When the minimization space is suitably decomposed into subspaces, two algorithms are proposed to solve the minimization problem. The f...
