Abstract
In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax=b is examined. The minimization of ||AM−I|| in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M. For symmetric positive definite A and a given a priori pattern there exist methods for computing factorized sparse approximate inverses L with LL T≈A −1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L.
We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test modifications of this method for computing factorized sparse approximate inverses.
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Huckle, T. Factorized Sparse Approximate Inverses for Preconditioning. The Journal of Supercomputing 25, 109–117 (2003). https://doi.org/10.1023/A:1023988426844
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DOI: https://doi.org/10.1023/A:1023988426844