Padé-type approximants and linear functional transformations

  • Claude Brezinski
  • Jeannette Van Iseghem
Approximation And Interpolation Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)


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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  1. 1.
    Brezinski, C., Padé type approximation and general orthogonal polynomials, Birkhäuser Verlag, Basel 1980.CrossRefzbMATHGoogle Scholar
  2. 2.
    Brochet, P., Contribution à l'inversion numérique de la transformée de Laplace …, Thèse 3e cycle, Université de Lille I, 1983.Google Scholar
  3. 3.
    Duc-Jacquet, M., Espaces hilbertiens à noyaux reproduisants, Lecture Notes, Université de Grenoble, 1979.Google Scholar
  4. 4.
    Iseghem, J. van, Applications des approximants de type Padé, Thèse 3e cycle, Université de Lille I, 1983.Google Scholar
  5. 5.
    Rossum, H. van, Generalized Padé approximants, in "Approximation Theory III", E.W. Cheney ed., Academic Press, New-York, 1980.Google Scholar
  6. 6.
    Sneddon, I.N., The use of integral transforms, Tata Mc Graw-Hill, New Delhi, 1974.zbMATHGoogle Scholar
  7. 7.
    Walsh, J.L., Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloqium Publ. XX, Providence, 1969.Google Scholar

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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