BIT Numerical Mathematics

, Volume 35, Issue 2, pp 169–201 | Cite as

Look-ahead in Bi-CGSTAB and other product methods for linear systems

  • C. Brezinski
  • M. Redivo-Zaglia


The Lanczos method for solvingAx = b consists in constructing the sequence of vectorsx k such thatr k =b − Ax k =P k (A)r0 whereP k is the orthogonal polynomial of degree at mostk with respect to the linear functionalc whose moments arec i ) =c i = (y, A i r0).

In this paper we discuss how to avoid breakdown and near-breakdown in a whole class of methods defined byr k =Q k (A)P k (A)r0,Q k being a given polynomial. In particular, the case of the Bi-CGSTAB algorithm is treated in detail. Some other choices of the polynomialsQ k are also studied.

Key words

Linear equations iterative methods 


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Copyright information

© BIT Foundation 1995

Authors and Affiliations

  • C. Brezinski
    • 1
  • M. Redivo-Zaglia
    • 2
  1. 1.Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA - M3Université des Sciences et Technologies de LilleCedexFrance
  2. 2.Dipartimento di Elettronica e InformaticaUniversità degli Studi di PadovaPadovaItaly

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