Zeros of Sobolev orthogonal polynomials following from coherent pairs
type: Item
instance of: scholarly article
title: Zeros of Sobolev orthogonal polynomials following from coherent pairs
zbMATH Open document ID: 1005.42015
DOI: 10.1016/S0377-0427(01)00421-6
published in: Journal of Computational and Applied Mathematics
publication date: 2002-05-21T00:00:00Z
review text: The location of the zeros of polynomials orthogonal with respect to an inner product involving derivatives (a Sobolev inner product) is not a simple question. Nevertheless, if the two measures involved in the inner product form a coherent pair, all the zeros of the Sobolev orthogonal polynomials are real and simple. In this paper the authors study their relative location, namely when they interlace with the zeros of standard orthogonal polynomials (Laguerre or Jacobi) or separate those of Sobolev orthogonal polynomials of lower degree. As in the classical case, Gauss quadrature proves to be a useful tool.
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1743073
zbMATH Keywords: Sobolev orthogonal polynomials
zbMATH Keywords: zeros
zbMATH Keywords: coherent pairs
zbMATH Keywords: Gauss quadrature
author: Henk Meijer
author: Marcel G. de Bruin
reviewed by: Andrei Martínez Finkelshtein
MaRDI profile type: Publication
cites work: On polynomials orthogonal with respect to certain Sobolev inner products
cites work: Laguerre-Sobolev orthogonal polynomials
cites work: Orthogonal polynomials and coherent pairs: The classical case
cites work: Coherent pairs and zeros of Sobolev-type orthogonal polynomials
cites work: Determination of all coherent pairs
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description: scientific article; zbMATH DE number 1743073