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Title: Continued fractions and orthogonal rational functions
Authors: Bultheel, Adhemar ×
González-Vera, Pablo
Hendriksen, Erik
Njåstad, Olav #
Issue Date: Jan-1998
Publisher: Marcel Dekker AG
Host Document: Proceedings of Orthogonal Functions, Moment Theory and Continued Fractions: Theory and Applications pages:69-100
Conference: Orthogonal Functions, Moment Theory and Continued Fractions: Theory and Applications location:Campinas, Brazil date:19-28 June 1996
Abstract: Given a modified PC fraction with approximants A_n/B_n there exists a unique pair (L_0,L_∞) of formal power series at 0 and ∞ such that A_{2m}/B_{2m} is the weak (m,m) two-point Padé approximant to L_0 of order m+1 and to L_∞ of order m, while A_{2m+1}/B_{2m+1} is the weak (m,m) two-point Padé approximant to L_∞ of order m and to L_∞ of order m+1. The canonical denominators of the even contraction of the modified PC fraction (which is a modified T fraction) are orthogonal Laurent polynomials obtained from the basis {1,1/z,z,1/z^2,z^2,...}, while the canonical denominators of the odd contractions of the modified PC fraction (which is a modified M fraction) are orthogonal Laurent polynomials obtained from the basis {1,z,1/z,z^2,1/z^2,...}.

An analogous situation arises when the pair of power series (L_0,L_∞) is replaced by Newton series determined by a general interpolation table of points on the real line, the modified PC fraction and its contractions are replaced by appropriate analogous continued fractions, and orthogonal Laurent polynomials are replaced by orthogonal rational functions with poles in the set of interpolation points. In this paper an investigation of these relationships is carried out.
Description: Lecture notes in pure and applied mathematics, vol. 199
URI: 
Publication status: published
KU Leuven publication type: IC
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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