Resumen de An approximate matrix inversion procedure by parallelization of the Sherman-Morrison formula

K. Moriya, Linjie Zhang, T. Nodera

• The Sherman�Morrison formula is one scheme for computing the approximate inverse preconditioner of a large linear system of equations. However, parallelizing a preconditioning approach is not straightforward as it is necessary to include a sequential process in the matrix factorization. In this paper, we propose a formula that improves the performance of the Sherman�Morrison preconditioner by partially parallelizing the matrix factorization. This study shows that our parallel technique implemented on a PC cluster system of eight processing elements significantly reduces the computational time for the matrix factorization compared with the time taken by a single processor. Our study has also verified that the Sherman�Morrison preconditioner performs better than ILU or MR preconditioners.