Recently Laurie presented a new algorithm for the computation of (2n+1)-point Gauss-Kronrod quadrature rules with real nodes and positive weights. This algorithm first determines a...
Daniela Calvetti, Gene H. Golub, William B. Gragg,...
— A form of Gauss-Quadrature rule over [0,1] has been investigated that involves the derivative of the integrand at the pre-assigned left or right end node. This situation arises...
: Given a probability measure and a positive integer n. How to choose n knots and n weights such that the corresponding quadrature rule has the minimum worst-case error when appli...
Abstract. In this paper we provide sharp bounds for the error in approximating the Riemann-Stieltjes integral R b a f (t) du (t) by the trapezoidal rule f (a) + f (b) 2 [u (b) u (a...
In this paper we introduce construction algorithms for Korobov rules for numerical integration which work well for a given set of dimensions simultaneously. The existence of such ...
Josef Dick, Friedrich Pillichshammer, Benjamin J. ...