A Hilbert transform representation of the error in Lagrange interpolation

被引：3

作者：

Kubayi, DG

Lubinsky, DS

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Univ Witwatersrand, Sch Math, ZA-2050 Wits, South Africa

来源：

JOURNAL OF APPROXIMATION THEORY | 2004年 / 129卷 / 01期

关键词：

Lagrange interpolation; Hilbert tranform;

D O I：

10.1016/j.jat.2004.05.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let L-n[f] denote the Lagrange interpolation polynomial to a function f at the zeros of a polynomial P-n with distinct real zeros. We show that f - L-n [f] = -PnHc [H[f]/(P-n) over bar], where H denotes the Hilbert transform, and H-e is an extension of it. We use this to prove convergence of Lagrange interpolation for certain functions analytic in (-1, 1) that are not assumed analytic in any ellipse with foci at (-1, 1). (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：94 / 100

页数：7

共 6 条

[1] The Bernstein constant and polynomial interpolation at the Chebyshev nodes [J].