Sparse Approximate Inverses and Target Matrices

Authors:
Ruth M. Holland;Andy J. Wathen;Gareth J. Shaw
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2005

Citing 0
Cited 6

Almost optimal order approximate inverse based preconditioners for 3-d convection dominated problems on tensor-grids

International Journal of Computing Science and Mathematics
Frobenius norm minimization and probing for preconditioning

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Smoothing and regularization with modified sparse approximate inverses

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Adaptive Pattern Research for Block FSAI Preconditioning

SIAM Journal on Scientific Computing
Banded target matrices and recursive FSAI for parallel preconditioning

Numerical Algorithms

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Abstract

If P has a prescribed sparsity and minimizes the Frobenius norm |I-PA|F, it is called a sparse approximate inverse of A. It is well known that the computation of such a matrix P is via the solution of independent linear least squares problems for the rows separately (and therefore in parallel). In this paper we consider the choice of other norms and introduce the idea of "target" matrices. A target matrix, T, is readily inverted and thus forms part of a preconditioner when |T-PA| is minimized over some appropriate sparse matrices P. The use of alternatives to the Frobenius norm which maintain parallelizability, while discussed in early literature, does not appear to have been exploited.