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Zbl 0927.65045
Huckle, Thomas
Approximate sparsity patterns for the inverse of a matrix and preconditioning. (English)
[J] Appl. Numer. Math. 30, No.2-3, 291-303 (1999). ISSN 0168-9274

The author shows that it is possible to use purely algebraic methods to derive a rough prediction for a sparsity pattern of a sparse approximate inverse matrix. Different strategies for choosing a-priori such patterns are compared. It is shown that the sparsity pattern can be used as a maximum pattern to distribute the claimed data in one step to each processor. Therefore, communication is necessary only at the beginning and at the end of a subprocess. Results of numerical experiments comparing the different methods with regard to the quality of the resulting approximation for the inverse are given.
[R.P.Tewarson (Stony Brook)]

MSC 2000:: *65F05 Direct methods for linear systems
65F35 Matrix norms, etc. (numerical linear algebra)
65F50 Sparse matrices

Keywords: sparse approximate inverse; preconditioning; numerical examples; sparsity pattern

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