\(S\)-orthogonality and construction of Gauss-Turán-type quadrature formulae
This paper gives a new method for constructing Gauss-Turán type quadrature formulae. To this purpose the authors use the theory of \(S\)-orthogonality and reinterprete it in terms of the standard orthogonal polynomials on the real line. For finding the nodes they consider an iterative method with quadratic convergence based on a discretized Stieltjes procedure and the Newton-Kantorovich method. The authors also present a numerical procedure for calculating the coefficients. Numerical examples are given.
scientific article; zbMATH DE number 1115933
scientific article