Convergence Theory of Restricted Multiplicative Schwarz Methods

Authors:
Reinhard Nabben;Daniel B. Szyld
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2002

Citing 0
Cited 4

On Hybrid Multigrid-Schwarz Algorithms

Journal of Scientific Computing
Parallel Two-Grid Semismooth Newton-Krylov-Schwarz Method for Nonlinear Complementarity Problems

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Overlapping restricted additive Schwarz method applied to the linear complementarity problem with an H-matrix

Computational Optimization and Applications
The Optimized Schwarz Method with a Coarse Grid Correction

SIAM Journal on Scientific Computing

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Abstract

Convergence results for the restricted multiplicative Schwarz (RMS) method, the multiplicative version of the restricted additive Schwarz (RAS) method for the solution of linear systems of the form Ax = b, are provided. An algebraic approach is used to prove convergence results for nonsymmetric M-matrices. Several comparison theorems are also established. These theorems compare the asymptotic rate of convergence with respect to the amount of overlap, the exactness of the subdomain solver, and the number of domains. Moreover, comparison theorems are given between the RMS and RAS methods as well as between the RMS and the classical multiplicative Schwarz method.