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Linear barycentric rational quadrature

Klein, Georges ; Berrut, Jean-Paul

In: BIT Numerical Mathematics, 2012, vol. 52, no. 2, p. 407-424

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    Title
    • Linear barycentric rational quadrature
    Author
    • Klein, Georges. Department of Mathematics, University of Fribourg, 1700, Pérolles, Fribourg, Switzerland
    • Berrut, Jean-Paul. Department of Mathematics, University of Fribourg, 1700, Pérolles, Fribourg, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:310529
    Summary
    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