Algebraic theory of multiplicative Schwarz methods

The convergence of multiplicative Schwarz-type methods for solving linear s ystems when the coefficient matrix is either a nonsingular M-matrix or a sy mmetric positive definite matrix is studied using classical and new results from the theory of splittings. The effect on convergence of algorithmic pa rameters such as the number of subdomains, the amount of overlap, the resul t of inexact local solves and of "coarse grid" corrections (global coarse s olves) is analyzed in an algebraic setting. Results on algebraic additive S chwarz are also included.