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BiCGstab(l) and other hybrid Bi-CG methods

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Abstract

It is well-known that Bi-CG can be adapted so that the operations withA T can be avoided, and hybrid methods can be constructed in which it is attempted to further improve the convergence behaviour. Examples of this are CGS, Bi-CGSTAB, and the more general BiCGstab(l) method. In this paper it is shown that BiCGstab(l) can be implemented in different ways. Each of the suggested approaches has its own advantages and disadvantages. Our implementations allow for combinations of Bi-CG with arbitrary polynomial methods. The choice for a specific implementation can also be made for reasons of numerical stability. This aspect receives much attention. Various effects have been illustrated by numerical examples.

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Authors and Affiliations

  1. Mathematical Institute, University of Utrecht, P.O. Box 80.010, NL-3508 TA, Utrecht, The Netherlands

    G. L. G. Sleijpen, H. A. van der Vorst & D. R. Fokkema

Authors
  1. G. L. G. Sleijpen
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  2. H. A. van der Vorst
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  3. D. R. Fokkema
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Communicated by C. Brezinski

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Sleijpen, G.L.G., van der Vorst, H.A. & Fokkema, D.R. BiCGstab(l) and other hybrid Bi-CG methods. Numer Algor 7, 75–109 (1994). https://doi.org/10.1007/BF02141261

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  • DOI: https://doi.org/10.1007/BF02141261

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