The use of rational functions in numerical quadrature

[摘要] Quadrature problems involving functions that have poles outside the interval of integration can profitably be solved by methods that are exact not only for polynomials of appropriate degree, but also for rational functions having the same (or the most important) poles as the function to be integrated. Constructive and computational tools for accomplishing this arc described and illustrated in a number of quadrature contexts. The superiority of such rational/polynomial methods is shown by an analysis of the remainder term and documented by numerical examples. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-08-01

[效力级别]  Proceedings Paper

[关键词] rational quadrature rules;remainder term;rational Fejer quadrature;rational Gauss;Gauss-Kronrod, and Gauss-Turan quadrature;rational quadrature rules for Cauchy principal value integrals