THE EXISTENCE AND CONSTRUCTION OF RATIONAL GAUSS-TYPE QUADRATURE RULES∗

Abstract. Consider a hermitian positive-definite linear functional F, and assume we have m distinct nodes fixed in advance anywhere on the real line. In this paper we then study the existence and construction of nth rational Gauss-Radau (m = 1) and Gauss-Lobatto (m = 2) quadrature formulas that approximate F{f}. These are quadrature formulas with n positive weights and with the n−m remaining nodes real and distinct, so that the quadrature is exact in a (2n−m)-dimensional space of rational functions. Key words. Quasi-orthogonal rational functions, generalized eigenvalue problem, positive ra-tional interpolatory quadrature rules. AMS subject classifications. 42C05, 65D32, 65F15 1. Introduction. Th