Approximation And Interpolation Theory

Rational Approximation and Interpolation

Volume 1105 of the series Lecture Notes in Mathematics pp 100-108

Date:

Padé-type approximants and linear functional transformations

  • Claude BrezinskiAffiliated withLaboratoire d'Analyse Numérique et d'Optimisation, Université de Lille I
  • , Jeannette Van IseghemAffiliated withLaboratoire d'Analyse Numérique et d'Optimisation, Université de Lille I

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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.