Weighted max norms, splittings, and overlapping additive Schwarz iterations |
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Authors: | Andreas Frommer Daniel B. Szyld |
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Affiliation: | Fachbereich Mathematik, Bergische Universit?t GH Wuppertal, Gauss-Strasse 20, D-42097 Wuppertal, Germany; e-mail: frommer@math.uni-wuppertal.de, DE Department of Mathematics, Temple University (038-16), 1805 N. Broad Street, Philadelphia, Pennsylvania 19122-6094, USA; e-mail: szyld@math.temple.edu, US
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Abstract: | Summary. Weighted max-norm bounds are obtained for Algebraic Additive Schwarz Iterations with overlapping blocks for the solution of Ax = b, when the coefficient matrix A is an M-matrix. The case of inexact local solvers is also covered. These bounds are analogous to those that exist using A-norms when the matrix A is symmetric positive definite. A new theorem concerning P-regular splittings is presented which provides a useful tool for the A-norm bounds. Furthermore, a theory of splittings is developed to represent Algebraic Additive Schwarz Iterations. This representation makes a connection with multisplitting methods. With this representation, and using a comparison theorem, it is shown that a coarse grid correction improves the convergence of Additive Schwarz Iterations when measured in weighted max norm. Received March 13, 1998 / Revised version received January 26, 1999 |
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Keywords: | Mathematics Subject Classification (1991):65F10 65F35 65M55 |
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