Construction of generalized Gauss-Turán quadrature rules for systems of arbitrary functions (Q1591958)

In this paper, which is connected with the work of \textit{J. Ma, V. Rokhlin}, and \textit{S. Wandzura} [SIAM J. Numer. Anal. 33, No. 3, 971-996 (1996; Zbl 0858.65015)], a numerical scheme for the construction of generalized Gauss-Turan quadrature, replacing polynomials with functions from a rather wide class, is presented. In a special case, this construction reduces itself to the construction of generalized Gauss quadrature rules given in the above cited paper. The performance of the algorithm is illustrated with several numerical examples.