TY - JOUR
T1 - On Inexact Preconditioners for Nonsymmetric Matrices
AU - Bai, Zhong Zhi
AU - Ng, Michael K.
N1 - Funding Information:
This author’s research was subsidized by The Special Funds for Major State Basic Research Projects G1999032803.
This author’s research was supported in part by RGC grants 7130/02P, 7046/03P, and 7035/04P.
Publisher copyright:
© 2005 Society for Industrial and Applied Mathematics
PY - 2005/1
Y1 - 2005/1
N2 - Inexact versions of the block-triangular preconditioned 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.
AB - Inexact versions of the block-triangular preconditioned 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.
KW - Block two-by-two matrices
KW - Minimal polynomial
KW - Preconditioners
UR - http://www.scopus.com/inward/record.url?scp=25444458272&partnerID=8YFLogxK
U2 - 10.1137/040604091
DO - 10.1137/040604091
M3 - Journal article
AN - SCOPUS:25444458272
SN - 1064-8275
VL - 26
SP - 1710
EP - 1724
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 5
ER -