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Quasilinear sequence transformations

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Abstract

We give a new characterization of quasilinear sequence transformations; we prove that any quasilinear transformation can be represented by its kernel. This approach is new and allows one to give a general result of convergence acceleration and tools for the construction of new quasilinear transformations.

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References

  1. A.C. Aitken, On Bernoulli's numerical solutions of algebraic equations, Proc. Roy. Soc. Edinburgh 46 (1926) 289–305.

    MATH  Google Scholar 

  2. M.D. Benchiboun, Etude de Certaines Généralisations du Procédé d'Aitken et Comparaison de Procédés d'Accélération de la Convergence, Thèse, Université de Lille 1 (1987).

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

    MathSciNet  Google Scholar 

  4. C. Brezinski, Quasilinear extrapolation processes, in: Numerical Mathematics, Singapore, 1988, International Series of Numerical Mathematics, Vol. 86, eds. R.P. Agarwal et al. (Birkhäuser, Basel, 1988) pp. 61–78.

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

  6. J. Dieudonné, Foundations of Modern Analysis (Academic Press, New York, 1960).

  7. B. Germain-Bonne, Transformations des suites, RAIRO, R1 (1973) 84–90.

  8. P. Henrici, Elements of Numerical Analysis (Wiley, New York, 1964).

  9. H. Sadok, Quasilinear vector extrapolation methods, Linear Algebra Appl. 140 (1993) 71–83.

  10. H. Sadok, About Henrici's transformation for accelerating vector sequences, J. Comput. Appl. Math. 29 (1990) 101–110.

    Article  MATH  MathSciNet  Google Scholar 

  11. P. Wynn, Acceleration techniques for iterated vector matrix problems, Math. Comput. 16 (1962) 301–322.

    MATH  MathSciNet  Google Scholar 

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Benazzouz, A. Quasilinear sequence transformations. Numerical Algorithms 15, 275–285 (1997). https://doi.org/10.1023/A:1019154106316

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  • DOI: https://doi.org/10.1023/A:1019154106316

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