An algebraic approach to certain differential eigenvalue problems
type: Item
instance of: scholarly article
title: An algebraic approach to certain differential eigenvalue problems
zbMATH Open document ID: 0854.33006
DOI: 10.1016/0024-3795(94)00198-7
author: A. M. Cohen
published in: Linear Algebra and its Applications
publication date: 1996-06-30T00:00:00Z
review text: The aim of the author is to derive a number of properties of the zeros of some orthogonal polynomials by considering only the recurrence relations satisfied by these polynomials. To this end he transforms first the known three-step recurrence relation connected with the given polynomial to a new recurrence relation which generates the characteristic polynomial of a symmetric tridiagonal matrix. Then he uses the already known properties of the eigenvalues of symmetric matrices. The method is explained on (and applied to) some particular polynomials such as Legendre, Krall-Legendre and Laguerre polynomials. For these polynomials he finds the intervals including the zeros, bounds for the zeros and approximations to the largest zeros. The paper includes also an example where the tridiagonal matrix is unsymmetric.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 894243
reviewed by: Mithat Idemen
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00198-7
OpenAlex ID: W1998990773
cites work: Q5185900
cites work: Q5674306
cites work: Differential operators and the Legendre type polynomials
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description: scientific article; zbMATH DE number 894243