Barycentric rational interpolation with no poles and high rates of approximation
Barycentric rational interpolation with no poles and high rates of approximation
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DOI：
10.1007/s00211-007-0093-y
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发表时间：
2007-08-01
影响因子：
2.1
通讯作者：
Hormann, Kai
中科院分区：
文献类型：
--
作者：
Floater, Michael S.;Hormann, Kai
众所周知，有理插值有时会比多项式插值提供更好的近似值，特别是对于较大的点序列，但很难控制极点的出现。在本文中，我们提出并研究了一系列重心有理插值器，它们在任何实数区间上都没有实极点和任意高的近似阶，而不管点的分布如何。这些插值线性依赖于数据，并包括 Berrut 的构造作为特例。
It is well known that rational interpolation sometimes gives better approximations than polynomial interpolation, especially for large sequences of points, but it is difficult to control the occurrence of poles. In this paper we propose and study a family of barycentric rational interpolants that have no real poles and arbitrarily high approximation orders on any real interval, regardless of the distribution of the points. These interpolants depend linearly on the data and include a construction of Berrut as a special case.