Numerical Algorithms

, Volume 3, Issue 1, pp 345–352 | Cite as

On higher order Padé-type approximants with some prescribed coefficients in the numerator

  • Miguel A. Piñar
  • Teresa E. Pérez
Article
  • 26 Downloads

Abstract

In this work, we consider the construction of higher order rational approximants to a formal power series, with some prescribed coefficients in their numerators, precisely those of the higher order powers. The denominators of such approximants are related to the so-called Sobolev-type orthogonal polynomials. The elementary properties of these orthogonal polynomials are studied in the regular case.

Subject classification

AMS (MOS) 33A65 

Keywords

Padé-type approximants Sobolev-type orthogonal polynomials 

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References

  1. [1]
    C. Brezinski,Padé-Type Approximation and General Orthogonal Polynomials, ISNM vol. 50 (Birkhäuser, Basel, 1980).Google Scholar
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    C. Brezinski, Partial Padé approximation, J. Approx. Theory 54 (1988) 210–233.CrossRefGoogle Scholar
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    F. Marcellán and A. Ronveaux, On a class of polynomials orthogonal with respect to a Sobolev inner product, Indag. Math. N.S. 1 (1990) 451–464.Google Scholar
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    G. Pólya and G. Szegö,Problems and Theorems in Analysis II (Springer, 1954).Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1992

Authors and Affiliations

  • Miguel A. Piñar
    • 1
  • Teresa E. Pérez
    • 1
  1. 1.Departamento de Matemática Aplicada, Facultad de CienciasUniversidad de GranadaGranadaSpain

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