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On Least-Squares Approximate Inverse-Based Preconditioners

In: Numerical Mathematics and Advanced Applications

Author

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  • B. Carpentieri

    (Karl-Franzens University, Institute of Mathematics and Scientific Computing)

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.

Suggested Citation

  • B. Carpentieri, 2008. "On Least-Squares Approximate Inverse-Based Preconditioners," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 159-166, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_18
    DOI: 10.1007/978-3-540-69777-0_18
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