The existence and construction of rational Gauss-type quadrature rules

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.nrpages: 27status: publishe

The existence and construction of rational Gauss-type quadrature rules

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.status: publishe