Rate of Convergence of Some Space Decomposition Methods for Linear and Nonlinear Problems

Abstract

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 differential 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.