TY - JOUR
T1 - DQGMRES
T2 - A direct quasi-minimal residual algorithm based on incomplete orthogonalization
AU - Saad, Yousef
AU - Wu Kesheng, Kesheng
PY - 1996
Y1 - 1996
N2 - We describe a Krylov subspace technique, based on incomplete orthogonalization of the Krylov vectors, which can be considered as a truncated version of GMRES. Unlike GMRES(m), the restarted version of GMRES, the new method does not require restarting. Like GMRES, it does not break down. Numerical experiments show that DQGMRES(k) often performs as well as the restarted GMRES using a subspace of dimension m = 2k. In addition, the algorithm is flexible to variable preconditioning, i.e., it can accommodate variations in the preconditioner at every step. In particular, this feature allows the use of any iterative solver as a right-preconditioner for DQGMRES(k). This inner-outer iterative combination often results in a robust approach for solving indefinite non-Hermitian linear systems.
AB - We describe a Krylov subspace technique, based on incomplete orthogonalization of the Krylov vectors, which can be considered as a truncated version of GMRES. Unlike GMRES(m), the restarted version of GMRES, the new method does not require restarting. Like GMRES, it does not break down. Numerical experiments show that DQGMRES(k) often performs as well as the restarted GMRES using a subspace of dimension m = 2k. In addition, the algorithm is flexible to variable preconditioning, i.e., it can accommodate variations in the preconditioner at every step. In particular, this feature allows the use of any iterative solver as a right-preconditioner for DQGMRES(k). This inner-outer iterative combination often results in a robust approach for solving indefinite non-Hermitian linear systems.
KW - GMRES
KW - Incomplete orthogonalization
KW - Iterative methods
KW - Krylov methods
KW - Quasiminimization
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U2 - 10.1002/(SICI)1099-1506(199607/08)3:4<329::AID-NLA86>3.0.CO;2-8
DO - 10.1002/(SICI)1099-1506(199607/08)3:4<329::AID-NLA86>3.0.CO;2-8
M3 - Article
AN - SCOPUS:21344474772
SN - 1070-5325
VL - 3
SP - 329
EP - 343
JO - Numerical Linear Algebra with Applications
JF - Numerical Linear Algebra with Applications
IS - 4
ER -