Numerical Algorithms

, Volume 1, Issue 2, pp 199–206 | Cite as

Avoiding breakdown in the CGS algorithm

  • Claude Brezinski
  • Hassane Sadok


The conjugate gradient squared algorithm can suffer of similar breakdowns as Lanczos type methods for the same reason that is the non-existence of some formal orthogonal polynomials. Thus curing such breakdowns is possible by jumping over these non-existing polynomials and using only those of them which exist. The technique used is similar to that employed for avoiding breakdowns in Lanczos type methods. The implementation of these new methods is discussed. Numerical examples are given.

Subject classifications

AMS (MOS) 65F10 65F25 


Lanczos method conjugate gradient squared algorithm orthogonal polynomials 


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Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1991

Authors and Affiliations

  • Claude Brezinski
    • 1
  • Hassane Sadok
    • 1
  1. 1.Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA-M3Université des Sciences et Techniques de LilleVilleneuve d'Ascq-CedexFrance

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