Algebraic Schwarz Theory
نویسنده
چکیده
This report contains a collection of notes on abstract additive and multiplicative Schwarz methods for self-adjoint positive linear operator equations. We examine closely one of the most elegant and useful modern convergence theories for these methods, following the recent work in the finite element multigrid and domain decomposition literature. Our motivation is to fully understand the structure of the existing theory, and then to examine whether generalizations can be constructed, suitable for analyzing algebraic multigrid and algebraic domain decomposition methods (as well as other methods), when no finite element structure is available. ∗ THIS WORK WAS SUPPORTED IN PART BY THE NSF UNDER COOPERATIVE AGREEMENT NO. CCR-9120008. THE GOVERNMENT HAS CERTAIN RIGHTS IN THIS MATERIAL.
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