Best approximation and interpolation of (1+(ax)2)-1 and its transforms

被引：14

作者：

Lubinsky, DS ^{[1
]}

机构：

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

来源：

JOURNAL OF APPROXIMATION THEORY | 2003年 / 125卷 / 01期

关键词：

interpolation; best approximation;

D O I：

10.1016/j.jat.2003.09.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that Lagrange interpolants at the Chebyshev zeros yield best relative polynomial approximations of (1 + (ax)(2))(-1) on [-1,1] and more generally of [GRAPHICS] where mu is a suitably restricted measure. We use this to study relative approximation of (1 + x(2))(-1) on an increasing sequence of intervals, and Lagrange interpolation of \x\(gamma). Moreover, we show how it gives a simple proof of identities for some trigonometric sums. (C) 2003 Published by Elsevier Inc.

引用

页码：106 / 115

页数：10