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On the Lebesgue constant of barycentric rational interpolation at equidistant nodes

机译:等距节点上重心有理插值的Lebesgue常数

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摘要

Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and important question concerns the condition of this rational approximation method. In this paper we extend a recent study of the Lebesgue function and constant associated with Berrut’s rational interpolant at equidistant nodes to the family of Floater–Hormann interpolants, which includes the former as a special case.
机译:最近的结果表明,由Floater和Hormann引入的重心有理插值族非常适合函数及其派生,积分和基元的逼近。尤其是在等距插值节点的情况下,这些无限平滑插值比其多项式类似物提供了更好的选择。一个自然而重要的问题涉及这种有理逼近方法的条件。在本文中,我们将等距节点上与贝鲁特有理插值相关的Lebesgue函数和常数的最新研究扩展到Floater-Hormann插值族,其中包括前者作为特例。

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  • 来源
    《Numerische Mathematik》 |2012年第3期|p.461-471|共11页
  • 作者单位

    Department of Computer Science, University of Verona, Strada le Grazie 15, 37134, Verona, Italy;

    Department of Pure and Applied Mathematics, University of Padua, Via Trieste 63, 35121, Padua, Italy;

    Faculty of Informatics, University of Lugano, Via Giuseppe Buffi 13, 6904, Lugano, Switzerland;

    Department of Mathematics, University of Fribourg, Chemin du Musée 23, 1700, Fribourg, Switzerland;

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  • 正文语种 eng
  • 中图分类
  • 关键词

    65D05; 65F35; 41A05; 41A20;

    机译:65D05;65F35;41A05;41A20;

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