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

• Autores: K. Moriya, Linjie Zhang, T. Nodera
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 51, Nº 1, 2009, págs. 1-9
• Idioma: inglés
• DOI: 10.1017/s1446181109000364
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• Resumen

  • 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.