Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials

Authors:
Hans Volkmer
Affiliations:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P. O. Box 413, Milwaukee, WI 53201, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Matrix analysis

Matrix analysis
Limit points of eigenvalues of truncated tridiagonal operators

Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications

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Abstract

Sequences {p"n}"n"="0^~ of polynomials, orthogonal with respect to signed measures, are associated with a class of differential equations including the Mathieu, Lame and Whittaker-Hill equation. It is shown that the zeros of p"n form sequences which converge to the eigenvalues of the corresponding differential equations. Moreover, interlacing properties of the zeros of p"n are found. Applications to the numerical treatment of eigenvalue problems are given.