Parallel Computation of Entries of ${A}^{-1}$
Patrick Amestoy, Iain Duff, Jean-Yves L’Excellent, François-Henry Rouet · SIAM Journal on Scientific Computing · 2015
In this paper, we consider the computation in parallel of several entries of the inverse of a large sparse matrix. We assume that the matrix has already been factorized by a direct method and that the factors are distributed. Entries are efficiently computed by exploiting sparsity of the right-hand sides and the solution vectors in the triangular solution phase. We demonstrate that in this setting, parallelism and computational efficiency are two contrasting objectives. We develop an efficient approach and show its efficiency on a general purpose parallel multifrontal solver.