Preconditioning techniques for nonsymmetric and indefinite linear systems

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The standard preconditioning techniques for conjugate gradient methods often fail for matrices that are indefinite and/or strongly nonsymmetric. The most common alterative considered for these cases are either to use expensive direct solvers or to resort to one of many techniques based on the normal equations. This paper examines several such alternatives and compares them. In particular an incomplete LQ factorization is proposed and some of its implementation details are described. A number of experiments are reported to compare these methods.

Original languageEnglish (US)
Pages (from-to)89-105
Number of pages17
JournalJournal of Computational and Applied Mathematics
Issue number1-2
StatePublished - Nov 1988
Externally publishedYes

Bibliographical note

Funding Information:
* Research supported by the National Science Foundation under Grants No. US NSF-MIP-8410110 and US NSF DCR85-09970, the US Department of Energy under Grant No. DOE DE-FGO2-85ER25001, by the US Air Force under Contract AFSOR-85-0211, and the IBM donation.


  • Indefinite linear systems
  • SSOR preconditioners
  • incomplete LQ factorization
  • least squares problems
  • normal equations
  • preconditioned conjugate gradient


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