IJPAM: Volume 55, No. 3 (2009)

TRIDIAGONAL MATRICES AND THE COMPUTATION
OF GAUSSIAN QUADRATURES

Qassem Al-Hassan
Department of Mathematics
University of Sharjah
P.O. Box 27272, Sharjah, UNITED ARAB EMIRATES
e-mail: [email protected]


Abstract.There is a close relation between tridiagonal matrices and orthogonal polynomials, this relation is founded upon a second-order homogeneous linear difference equation that serves as a recursion relation used for generating these polynomials. This relation among tridiagonal matrices, orthogonal polynomials, and second-order homogeneous linear difference equations is employed in order to compute the nodes and weights of Gaussian quadratures.

Received: May 5, 2008

AMS Subject Classification: 65D32, 65Q05, 39A05, 65F15

Key Words and Phrases: tridiagonal matrices, Guassian quadrature, nodes and weights, recurrence relations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 3