A flexible inner-outer preconditioned GMRES algorithm. (English) Zbl 0780.65022

Saad, Youcef

SIAM J. Sci. Comput. 14, No. 2, 461-469 (1993).

The generalized minimal residual (GMRES) algorithm is modified so that it allows the change of preconditioner in every step. Since the GMRES algorithm does explicit orthogonalization of all iterates in every step, this presents no essential difficulty. The property that the residual is minimized in every step is preserved. There is no additional cost in the arithmetics but the memory requirements doubles. In particular, the generalized GMRES allows several steps of another iterative method (even GMRES itself) to be used as the preconditioner. Computational results are presented.

Reviewer: J.Mandel (Denver)

MSC:

65F10

Iterative numerical methods for linear systems

Keywords:

Krylov subspace methods; non-Hermitian systems; conjugate gradients; generalized minimal residual algorithm; preconditioner; GMRES algorithm; iterative method; Computational results