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Approximate sparsity patterns for the inverse of a matrix and preconditioning. (English) Zbl 0927.65045
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.
65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
65F50Sparse matrices (numerical linear algebra)