On Least-Squares Approximate Inverse-Based Preconditioners

B. Carpentieri ()
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B. Carpentieri: Karl-Franzens University, Institute of Mathematics and Scientific Computing

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 159-166 from Springer

Abstract: Abstract We discuss approximate inverse preconditioners based on Frobenius-norm minimization. We introduce a novel adaptive algorithm based on truncated Neumann matrix expansions for selecting the sparsity pattern of the preconditioner. The construction of the approximate inverse is based on a dual dropping strategy, namely a threshold to drop small entries and a maximum number of nonzero entries per column. We introduce a post-processing stabilization technique to deflate some of the smallest eigenvalues in the spectrum of the preconditioned matrix which can potentially disturb the convergence. Results of preliminary experiments are reported on a set of linear systems arising from different application fields to illustrate the potential of the proposed algorithm for preconditioning effectively iterative Krylov solvers.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_18

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DOI: 10.1007/978-3-540-69777-0_18

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