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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.
MSC:
65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
65F50Sparse matrices (numerical linear algebra)