Parallel computation of the diagonal of the inverse of a sparse matrix

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2017
Fasllija, Edona
We consider the parallel computation of the diagonal of the inverse of a large sparse matrix. This problem is critical in many applications such as quantum mechanics and uncertainty quantification, where a subset of the entries of the inverse matrix, usually the diagonal, is required. A straightforward approach involves inverting the matrix explicitly and extracting the diagonal of the computed inverse. This approach, however, almost always is too costly for large sparse matrices since the inverse is often dense. In this thesis, we develop a novel parallel algorithm for computing the diagonal of the inverse based on the parallel DS factorization and approximate inverse techniques combined with a special structural dropping strategy step that exploits the peculiar sparsity pattern of the S matrix. We analyze the parallel scalability and performance of the proposed algorithm using sparse matrices from various applications. 
Citation Formats
E. Fasllija, “Parallel computation of the diagonal of the inverse of a sparse matrix,” M.S. - Master of Science, Middle East Technical University, 2017.