Geodesic
Alternative orthogonal polynomials and quadratures
Electronic transactions on numerical analysis, Tome 25 (2006), pp. 17-26
A bidirectional orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0, 1] with the weighting function 1. Functional and recurrent relations are derived for the sequences that are the result of inverse orthogonalization procedure. Quadratures, generating by the sequences, are described. An example on approximation of the Cauchy problem is given.
Classification : 33C45
Keywords: orthogonal polynomial, recurrence relation, quadrature, initial value problem 
@article{ETNA_2006__25__a31,
     author = {Chelyshkov,  Vladimir S.},
     title = {Alternative orthogonal polynomials and quadratures},
     journal = {Electronic transactions on numerical analysis},
     pages = {17--26},
     year = {2006},
     volume = {25},
     zbl = {1107.33006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a31/}
}
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%A Chelyshkov,  Vladimir S.
%T Alternative orthogonal polynomials and quadratures
%J Electronic transactions on numerical analysis
%D 2006
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Chelyshkov,  Vladimir S. Alternative orthogonal polynomials and quadratures. Electronic transactions on numerical analysis, Tome 25 (2006), pp. 17-26. http://geodesic.mathdoc.fr/item/ETNA_2006__25__a31/