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Avoiding breakdown in the CGS algorithm

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Abstract

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.

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA-M3, Université des Sciences et Techniques de Lille, Flandres-Artois, 59655, Villeneuve d'Ascq-Cedex, France

    Claude Brezinski & Hassane Sadok

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  1. Claude Brezinski
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  2. Hassane Sadok
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Brezinski, C., Sadok, H. Avoiding breakdown in the CGS algorithm. Numer Algor 1, 199–206 (1991). https://doi.org/10.1007/BF02142321

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  • DOI: https://doi.org/10.1007/BF02142321

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