On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients-Reference-Cited by-同舟云学术

On Symmetric (1, 1)-Coherent Pairs and Sobolev Orthogonal polynomials: an algorithm to compute Fourier coefficients

Published:2019-07-01 Issue:2 Volume:53 Page:139-164
ISSN:2357-4100
Container-title:Revista Colombiana de Matemáticas
language:
Short-container-title:rev.colomb.mat

Author:

Dueñas Ruiz Herbert,Marcellán Francisco,Molano Alejandro

Abstract

In the pioneering paper [13], the concept of Coherent Pair was introduced by Iserles et al. In particular, an algorithm to compute Fourier Coefficients in expansions of Sobolev orthogonal polynomials defined from coherent pairs of measures supported on an infinite subset of the real line is described. In this paper we extend such an algorithm in the framework of the so called Symmetric (1, 1)-Coherent Pairs presented in [8].

Publisher

Universidad Nacional de Colombia

Subject

General Mathematics

Reference20 articles.

1. P. Althammer, Eine erweiterung des orthogonalitatsbegriffes bei polynomen und deren anwendung auf die beste approximation, J. Reine Angew. Math. 211 (1962), 192-204.

2. A. C. Berti and A. Sri Ranga, Companion orthogonal polynomials: some applications, Appl. Numer. Math. 39 (2001), 127-149.

3. C. Brezinski, A direct proof of the Christoffel-Darboux identity and its equivalence to the recurrence relationship, J Comput Appl Math. 32 (1990), no. 1, 17-25.

4. T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, 1978.

5. M. N. de Jesús, F. Marcellán, J. Petronilho, and N. Pinzón-Cortés, (M, N)-coherent pairs of order (m, k) and Sobolev orthogonal polynomials, J. Comput. Appl. Math. 256 (2014), 16-35.

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