Domain-Decomposition-Type Methods for Computing the Diagonal of a Matrix Inverse

Abstract

This paper presents two methods based on domain decomposition concepts for determining the diagonal of the inverse of a sparse matrix. The first uses a divide-and-conquer principle and the ShermanMorrison-Woodbury formula, and assumes that the matrix can be decomposed into a 2 × 2 block-diagonal matrix and a low-rank matrix. The second method is a standard… (More)
DOI: 10.1137/100799939

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