BIT Numerical Mathematics

, Volume 52, Issue 2, pp 407–424 | Cite as

Linear barycentric rational quadrature

Article

Abstract

Linear interpolation schemes very naturally lead to quadrature rules. Introduced in the eighties, linear barycentric rational interpolation has recently experienced a boost with the presentation of new weights by Floater and Hormann. The corresponding interpolants converge in principle with arbitrary high order of precision. In the present paper we employ them to construct two linear rational quadrature rules. The weights of the first are obtained through the direct numerical integration of the Lagrange fundamental rational functions; the other rule, based on the solution of a simple boundary value problem, yields an approximation of an antiderivative of the integrand. The convergence order in the first case is shown to be one unit larger than that of the interpolation, under some restrictions. We demonstrate the efficiency of both approaches with numerical tests.

Keywords

Rational interpolation Barycentric form Quadrature 

Mathematics Subject Classification (2000)

65D05 65D32 41A05 41A20 41A25 

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Copyright information

© Springer Science + Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FribourgPérollesSwitzerland

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