On the Lebesgue constant of Berrut's rational interpolant at equidistant nodes

被引：34

作者：

Bos, Len ^{[2
]}

De Marchi, Stefano ^{[3
]}

Hormann, Kai ^{[1
]}

机构：

[1] Univ Lugano, Lugano, Switzerland

[2] Univ Verona, I-37100 Verona, Italy

[3] Univ Padua, I-35100 Padua, Italy

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 236卷 / 04期

关键词：

Rational interpolation; Lebesgue constant; Equidistant nodes;

D O I：

10.1016/j.cam.2011.04.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut's rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results suggest that the Lebesgue constant behaves similarly for interpolation at Chebyshev as well as logarithmically distributed nodes. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：504 / 510

页数：7

共 11 条

[1] Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval [J].