Geodesic
Orthogonal polynomials and quadrature
Electronic transactions on numerical analysis, Tome 9 (1999), pp. 65-76
Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality encountered in Tur$\acute $an-type quadratures. Relevant questions of numerical computation are also considered.
Classification : 33C45, 65D32, 65F15
Keywords: orthogonal polynomials, Gauss-lobatto, Gauss-kronrod, and Gauss-tur$\acute $an rules, computation of Gauss-type quadrature rules 
@article{ETNA_1999__9__a6,
     author = {Gautschi,  Walter},
     title = {Orthogonal polynomials and quadrature},
     journal = {Electronic transactions on numerical analysis},
     pages = {65--76},
     year = {1999},
     volume = {9},
     zbl = {0963.33004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1999__9__a6/}
}
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Gautschi,  Walter. Orthogonal polynomials and quadrature. Electronic transactions on numerical analysis, Tome 9 (1999), pp. 65-76. http://geodesic.mathdoc.fr/item/ETNA_1999__9__a6/