Geodesic
Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line
Electronic transactions on numerical analysis, Tome 19 (2005), pp. 113-134
The purpose of this paper is the computation of quadrature formulas based on Laurent polynomials in two particular situations: the Real Half-Line and the Unit Circle. Comparative results and a connection with the split Levinson algorithm are established. Illustrative numerical examples are approximate integrals of the form 1 f (x) $\omega (x)$ dx , r = 1, 2, 3, . . .
Classification : 41A55, 33C45, 65D30
Keywords: orthogonal Laurent polynomials, L-Gaussian quadrature, szeg $\ddot o$ quadrature, three-term recurrence relations, split levinson algorithm, numerical quadrature 
@article{ETNA_2005__19__a0,
     author = {Cruz-Barroso,  Ruym\'an and Gonz\'alez-Vera,  Pablo},
     title = {Orthogonal {Laurent} polynomials and quadratures on the unit circle and the real half-line},
     journal = {Electronic transactions on numerical analysis},
     pages = {113--134},
     year = {2005},
     volume = {19},
     zbl = {1092.42015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2005__19__a0/}
}
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Cruz-Barroso,  Ruymán; González-Vera,  Pablo. Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line. Electronic transactions on numerical analysis, Tome 19 (2005), pp. 113-134. http://geodesic.mathdoc.fr/item/ETNA_2005__19__a0/