Convergence Theory of Restricted Multiplicative Schwarz Methods

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.

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