Volume 3, pp. 96-115, 1995.

Gaussian quadrature for matrix valued functions on the unit circle

Ann Sinap

Abstract

The Gaussian quadrature formulas for matrix valued functions on the unit circle are described. It is shown how the eigenvalues and eigenvectors of a unitary lower block Hessenberg matrix can be used to compute an approximation of a given matrix integral on the unit circle. A parallel algorithm for this purpose has been implemented on a IBM SP1 and some examples are worked out.

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Key words

orthogonal matrix polynomials, block Hessenberg matrices, quadrature, parallel algorithm.

AMS subject classifications

42C05, 41A55, 47A56, 65D32, 65Y05.

ETNA articles which cite this article

Vol. 14 (2002), pp. 127-141 F. Marcellán and H. O. Yakhlef: Recent trends on analytic properties of matrix orthonormal polynomials

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