Title: Gaussian quadrature for multiple orthogonal polynomials
Authors: Coussement, Jonathan ×
Van Assche, Walter #
Issue Date: 2005
Publisher: Elsevier science bv
Series Title: Journal of computational and applied mathematics vol:178 issue:1-2 pages:131-145
Abstract: We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r + 1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix L-n, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of L, (c) 2004 Elsevier B.V. All rights reserved.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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