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    Bagci, Hakan (1)
    Pasciak, Joseph E. (1)
    Sirenko, Kostyantyn (1)
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    A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations

    Bagci, Hakan; Pasciak, Joseph E.; Sirenko, Kostyantyn (Numerical Linear Algebra with Applications, Wiley, 2014-11-11) [Article]
    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.
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