Padé-type approximants and linear functional transformations

  • Claude Brezinski
  • Jeannette Van Iseghem
Approximation And Interpolation Theory

DOI: 10.1007/BFb0072402

Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)
Cite this paper as:
Brezinski C., Van Iseghem J. (1984) Padé-type approximants and linear functional transformations. In: Graves-Morris P.R., Saff E.B., Varga R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg

Abstract

Let f(.)=\(\mathop \Sigma \limits_{i = o}^\infty\) cigi (.) be a series of functions and let F(.)=\(\mathop \Sigma \limits_{i = o}^\infty\) cihi (.) be the series obtained by applying a linear functional transformation to f. It is shown that the Padé-type approximants of F can be deduced from that of f by application of the same functional transform. Some examples and applications are given. Convergence theorems are obtained. The particular case of the Laplace transform is studied in more detail.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Claude Brezinski
    • 1
  • Jeannette Van Iseghem
    • 1
  1. 1.Laboratoire d'Analyse Numérique et d'OptimisationUniversité de Lille IVilleneuve d'Ascq CedexFrance

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