Geodesic
Gauss-Kronrod quadrature formulae. A survey of fifty years of research
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 371-404.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Kronrod in 1964, trying to estimate economically the error of the $n$-point Gauss quadrature formula for the Legendre weight function, developed a new formula by adding to the $n$ Gauss nodes $n+1$ new ones, which are determined, together with all weights, such that the new formula has maximum degree of exactness. It turns out that the new nodes are zeros of a polynomial orthogonal with respect to a variable-sign weight function, considered by Stieltjes in 1894, without though making any reference to quadrature. We survey the considerable research work that has been emerged on this subject, during the past fifty years, after Kronrod's original idea.
Classification : 65D32, 33C45
Keywords: Gauss quadrature formula, Gauss-kronrod quadrature formula, Stieltjes polynomials 
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     title = {Gauss-Kronrod quadrature formulae. {A} survey of fifty years of research},
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Notaris, Sotirios E. Gauss-Kronrod quadrature formulae. A survey of fifty years of research. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 371-404. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a6/