DQGMRES: A direct quasi-minimal residual algorithm based on incomplete orthogonalization

Yousef Saad, Kesheng Wu Kesheng

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)329-343
Number of pages15
JournalNumerical Linear Algebra with Applications
Issue number4
StatePublished - 1996


  • Incomplete orthogonalization
  • Iterative methods
  • Krylov methods
  • Quasiminimization


Dive into the research topics of 'DQGMRES: A direct quasi-minimal residual algorithm based on incomplete orthogonalization'. Together they form a unique fingerprint.

Cite this