The existence and construction of rational Gauss-type quadrature rules

Consider a hermitian positive-definite linear functional FF, 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 n  th rational Gauss–Radau (m=1)(m=1) and Gauss–Lobatto (m=2)(m=2) quadrature formulas that approximate F{f}F{f}. These are quadrature formulas with n   positive weights and with the n-mn-m remaining nodes real and distinct, so that the quadrature is exact in a (2n-m)(2n-m)-dimensional space of rational functions. Further, we also consider the case in which the functional is defined by a positive bounded Borel measure on an interval, for which it is required in addition that the nodes are all in the support of the measure.