BLOCK APPROXIMATE INVERSE PRECONDITIONERS FOR SPARSE NONSYMMETRIC LINEAR SYSTEMS
Juana Cerdán Soriano, Táher Faraj El Guelei, Natalia Malla Martínez, José Marı́n, José Mas · ETNA - Electronic Transactions on Numerical Analysis · 2010
In this paper block approximate inverse preconditioners to solve sparse nonsymmetric linear systems with iterative Krylov subspace methods are studied. The computation of the preconditioners involves consecutive updates of variable rank of an initial and nonsingular matrix and the application of the Sherman-Morrison- Woodbury formula to compute an approximate inverse decomposition of the updated matrices. Therefore, they are generalizations of the preconditioner presented in Bru et al. (SIAM J. Sci. Comput., 25 (2003), pp. 701-715). The stability of the preconditioners is studied and it is shown t hat their computation is breakdown-free for H-matrices. To test the performance the results of numerical experiments obtained for a representative set of matrices are presented.