Abstract. The convergence of multiplicative Schwarz-type methods for solving linear systems when the coefficient matrix is either a nonsingular M-matrix or a symmetric positive definite matrix is studied using classical and new results from the theory of splittings. The effect on convergence of algorithmic parameters such as the number of subdomains, the amount of overlap, the result of inexact local solves and of "coarse grid " corrections (global coarse solves) is analyzed in an algebraic setting. Some results on algebraic additive Schwarz are also included. Key words. Linear systems, M-matrix, symmetric positive definite matrix, multiplicative Schwarz, weighted max norms, splittings, comparison theorems, overlap, coarse grid correction. AMS(MOS) subject classification. 65F10, 65F35, 65M55.
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