On Inexact Preconditioners for Nonsymmetric Matrices

Abstract

Inexact versions of the block-triangular preconditioners for nonsymmetric matrices of block two-by-two structures in [M. F. Murphy, G. H. Golub, and A. J. Wathen, SIAM J. Sci. Comput., 21 (2000), pp. 1969--1972] and [I. C. F. Ipsen, SIAM J. Sci. Comput., 23 (2001), pp. 1050--1051] are presented, and the two preconditioners for symmetric block two-by-two matrices in [C. Durazzi and V. Ruggiero, Numer. Linear Algebra Appl., 10 (2003), pp. 673--688] are extended to general nonsymmetric matrices. Moreover, we precisely describe the spectral properties of the preconditioned matrices and the finite-step termination properties of the preconditioned Krylov subspace iteration methods with an optimal or Galerkin property, with respect to these preconditioners. Several numerical examples are performed to illustrate the effectiveness of the proposed preconditioners.