Multiplicative and additive Schwarz methods are two main classes of iterative methods since the times of Gauss and Jacobi. Traditionally the analyses of these two classes of methods follow different paths. On one hand, the theory for additive Schwarz methods [2, 6, 8,9, 11-16], like the theory for the classical Jacobi method, is relatively simple. On the other hand, the theory for multiplicative Schwarz methods [1, 3, 4, 9-11, 13, 15-19], like the theory for the classical Gauss-Seidel method, can be quite sophisticated.
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