Abstract
The aim of this paper is to give some convergence results for some sequences of generalized Padé-type approximants. We will consider two types of interpolatory functionals: one corresponding to Langrange and Hermite interpolation and the other corresponding to orthogonal expansions. For these two cases we will give sufficient conditions on the generating functionG(x, t) and on the linear functionalc in order to obtain the convergence of the corresponding sequence of generalized Padé-type approximants. Some examples are given.
Similar content being viewed by others
References
G.A. Baker Jr. and P. Graves-Morris,Padé Approximants, Part II, Encyclopedia of Mathematics and its Applications (Addison Wesley, Reading, MA, 1981).
C. Brezinski,Biorthogonality and its Applications to Numerical Analysis (Marcel Dekker, New York, 1991).
P.J. Davis,Interpolation and Approximation (Dover, New York, 1975).
Z. Rocha, Applications de la théorie de la biorthogonalité, Thèse, Université des Sciences et Technologies de Lille (1994).
G. Szegö,Orthogonal Polynomials, American Mathematical Society, Colloquium Publications Vol. 23 (AMS, Providence, 1938).
J.L. Walsh,Interpolation and Approximation by Rational Functions in the Complex Domain, Amercan Mathematical Society, Colloquium Publications Vol. 20 (AMS, Providence, 1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Matos, A.C. Some convergence results for the generalized Padé-type approximants. Numer Algor 11, 255–269 (1996). https://doi.org/10.1007/BF02142501
Issue Date:
DOI: https://doi.org/10.1007/BF02142501