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

In this paper, which is connected with the work of Ma, Rokhlin and Wandzura [1], a numerical scheme for the construction of generalized Gauss-Turán quadrature, replacing the 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 [1]. The performance of the algorithm is illustrated with several numerical examples.