Numerical Algorithms

, Volume 3, Issue 1, pp 75–80 | Cite as

Some vector sequence transformations with applications to systems of equations

  • C. Brezinski
  • H. Sadok


First, recursive algorithms for implementing some vector sequence transformations are given. In a particular case, these transformations are generalizations of Shanks transformation and the G-transformation. When the sequence of vectors under transformation is generated by linear fixed point iterations, Lanczos' method and the CGS are recovered respectively. In the case of a sequence generated by nonlinear fixed point iterations, a quadratically convergent method based on the ε-algorithm is recovered and a nonlinear analog of the CGS method is obtained.

Subject classification

AMS (MOS) 65B05 65F10 65F25 


Vector sequence extrapolation Lanczos method 


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Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1992

Authors and Affiliations

  • C. Brezinski
    • 1
  • H. Sadok
    • 1
  1. 1.Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA-M3Université des Sciences et Technologies de LilleVilleneuve d'Ascq-CedexFrance

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