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Some vector sequence transformations with applications to systems of equations

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Abstract

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.

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References

  1. C. Brezinski,Accélération de la Convergence en Analyse Numerique, Lecture Notes in Mathematics vol. 584 (Springer, Berlin, 1977).

    Google Scholar 

  2. C. Brezinski, Généralisations de la transformation de Shanks, de la table de Padé et de l' ε-algorithme, Calcolo 12 (1975) 317–360.

    Google Scholar 

  3. C. Brezinski,Padé-type Approximation and General Orthogonal, Polynomials Birkhäuser, Basel, 1980.

    Google Scholar 

  4. C. Brezinski, Some determinatal identities in a vector space, with applications, inPadé Approximation and its Applications, eds. H. Werner et al., Lecture Notes in Mathematics, vol. 1071 (Springer, Berlin, 1984).

    Google Scholar 

  5. C. Brezinski and M. Redivo Zaglia, A new presentation of orthogonal polynomials with applications to their computation, Numer. Algorithms 1 (1991) 207–221.

    Google Scholar 

  6. C. Brezinski and M. Redivo Zaglia,Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1991).

    Google Scholar 

  7. C. Brezinski and H. Sadok, Lanczos type methods for systems of linear equations, submitted.

  8. H. Le Ferrand, Convergence of the topological ε-algorithm for solving systems of nonlinear equations, Numer. Algorithms, this volume.

  9. W.C. Pye and T.A. Atchison, An algorithm for the computation of higher order G-transformation, SIAM J. Numer. Anal. 10 (1973) 1–7.

    Article  Google Scholar 

  10. P. Sonneveld, CGS, a fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Stat. Comp. 10 (1989) 36–52.

    Article  Google Scholar 

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Authors and Affiliations

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

    C. Brezinski & H. Sadok

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  1. C. Brezinski
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  2. H. Sadok
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Brezinski, C., Sadok, H. Some vector sequence transformations with applications to systems of equations. Numer Algor 3, 75–80 (1992). https://doi.org/10.1007/BF02141917

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