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DQGMRES: a Direct Quasi‐minimal Residual Algorithm Based on Incomplete Orthogonalization
Author(s) -
Saad Yousef,
Wu Kesheng
Publication year - 1996
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199607/08)3:4<329::aid-nla86>3.0.co;2-8
Subject(s) - generalized minimal residual method , orthogonalization , preconditioner , krylov subspace , solver , mathematics , linear system , iterative method , algorithm , residual , dimension (graph theory) , mathematical optimization , combinatorics , mathematical analysis
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 =2 k . 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.