Orthogonal rational functions and quadrature on the real half line.
The notion of orthogonal Laurent polynomials is extended to orthogonal rational functions. The rational functions have prescribed poles which can be thought of as poles grouped around zero and infinity. The orthogonal rational functions give rise to quadrature rules of Gaussian flavour, and the weights of the \(n\)-point Gauss-type quadrature formula are given explicitly. Errors and convergence for these Gauss-type formulas is handled in detail. The connection is made with multipoint Padé approximation. The paper is somewhat strange in this particular journal since no complexity issues are considered.
scientific article; zbMATH DE number 1967204
scientific article