Geodesic
Computation of Gauss-Kronrod quadrature rules with non-positive weights
Electronic transactions on numerical analysis, Tome 9 (1999), pp. 26-38
Recently Laurie presented a fast algorithm for the computation of (2n + 1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. We describe modifications of this algorithm that allow the computation of Gauss-Kronrod quadrature rules with complex conjugate nodes and weights or with real nodes and positive and negative weights.
Classification : 65D32, 65F15, 65F18
Keywords: orthogonal polynomials, indefinite measure, fast algorithm, inverse eigenvalue problem 
@article{ETNA_1999__9__a10,
     author = {Ammar,  G.S. and Calvetti,  D. and Reichel,  L.},
     title = {Computation of {Gauss-Kronrod} quadrature rules with non-positive weights},
     journal = {Electronic transactions on numerical analysis},
     pages = {26--38},
     year = {1999},
     volume = {9},
     zbl = {0954.65017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1999__9__a10/}
}
TY  - JOUR
AU  - Ammar,  G.S.
AU  - Calvetti,  D.
AU  - Reichel,  L.
TI  - Computation of Gauss-Kronrod quadrature rules with non-positive weights
JO  - Electronic transactions on numerical analysis
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EP  - 38
VL  - 9
UR  - http://geodesic.mathdoc.fr/item/ETNA_1999__9__a10/
LA  - en
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%A Reichel,  L.
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%J Electronic transactions on numerical analysis
%D 1999
%P 26-38
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%U http://geodesic.mathdoc.fr/item/ETNA_1999__9__a10/
%G en
%F ETNA_1999__9__a10
Ammar,  G.S.; Calvetti,  D.; Reichel,  L. Computation of Gauss-Kronrod quadrature rules with non-positive weights. Electronic transactions on numerical analysis, Tome 9 (1999), pp. 26-38. http://geodesic.mathdoc.fr/item/ETNA_1999__9__a10/