1. A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations.
- Author
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Bağcı, Hakan, Pasciak, Joseph E., and Sirenko, Kostyantyn Y.
- Subjects
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STOCHASTIC convergence , *LINEAR equations , *ITERATIVE methods (Mathematics) , *GAUSSIAN function , *APPROXIMATION theory , *CARTESIAN coordinates - Abstract
We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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