Efficient parallel processing technique for inverting matrices with random sparsity

Abstract
Algorithms for ordering a sparse matrix A for parallel triangular factorisation and for obtaining the parallel inverse of A are given. The heuristic ordering method is based on graph manipulations. It attempts to minimise the completion time of parallel triangular factorisation while preserving the sparsity of the matrix. The inversion method proposed is based on the triangular factors of A. The task of obtaining the ‘sparse inverse’of A is represented by a directed acyclic graph. The algorithm and the graph for the full inversion of A are also given. Claims are substantiated by experiments using test data from several electric networks.

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