Author:

Keywords:

Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Quasi-orthogonal rational functions, Generalized eigenvalue problem, Positive rational interpolatory quadrature rules, COMPLEX POLES, EIGENVALUE PROBLEMS, FORMULAS, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0802 Computation Theory and Mathematics, Numerical & Computational Mathematics, 4901 Applied mathematics, 4903 Numerical and computational mathematics

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.