A Sharp Convergence Estimate on the Method of Subspace Correction for Singular Systems

Young-Ju Lee

Department of Mathematics, Eberly College of Science
The Pennsylvania State University, 218 McAllister Building, University Park PA 16802-6401

Jinbiao Wu
Jinchao Xu
Ludmil Zikatanov


We shall present a sharp result on the convergence rate of the method of successive subspace corrections for singular system of equations. The result has been obtained for variational problems on a Hilbert space. Various identities for the convergence rate are presented especially for multigrid method and domain decomposition method. Some illustrations of theory are also given for problems posed on a finite dimensional Hilbert space.