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Indexed by:期刊论文

Date of Publication:2004-09-01

Journal:Journal of Information and Computational Science

Included Journals:Scopus、EI

Volume:1

Issue:1

Page Number:103-106

ISSN No.:15487741

Key Words:Integration; Invariance; Matrix algebra; Numerical methods, Bivariate orthogonal polynomials; Common zeros; Eigenfunction; Invariant factor; Jacobi matrix; Orthogonal polynomials of two variables; Stieltjes type theorems, Polynomials

Abstract:Some new properties with respect to bivariate orthogonal polynomials are studied from an invariant factor point of view. The main result states if the zeros of the invariant factor   ky(x) are distinct, then   ky(x) is the eigenfunction of the corresponding truncated Jacobi matrix. We shall also present a detailed investigation of the location of the common zeros of bivariate orthogonal polynomials. A simple application to cubature formulae is given in the end. Most of them can be regarded as the extension of the univariate cases. The results also offer a new method for studying bivariate orthogonal polynomials.