Geodesic
Gaussian quadrature for matrix valued functions on the unit circle
Electronic transactions on numerical analysis, Tome 3 (1995), pp. 96-115
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.
Classification : 42C05, 41A55, 47A56, 65D32, 65Y05
Keywords: orthogonal matrix polynomials, block hessenberg matrices, quadrature, parallel algorithm 
@article{ETNA_1995__3__a3,
     author = {Sinap,  Ann},
     title = {Gaussian quadrature for matrix valued functions on the unit circle},
     journal = {Electronic transactions on numerical analysis},
     pages = {96--115},
     year = {1995},
     volume = {3},
     zbl = {0868.42012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1995__3__a3/}
}
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%J Electronic transactions on numerical analysis
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Sinap,  Ann. Gaussian quadrature for matrix valued functions on the unit circle. Electronic transactions on numerical analysis, Tome 3 (1995), pp. 96-115. http://geodesic.mathdoc.fr/item/ETNA_1995__3__a3/