Best L1 approximation of Heaviside-type functions from Chebyshev and weak-Chebyshev spaces

被引：2

作者：

Gajny, Laurent ^{[1
]}

Gibaru, Olivier ^{[1
,2
]}

Nyiri, Eric ^{[1
]}

Fang, Shu-Cherng ^{[3
]}

机构：

[1] CNRS, UMR 7296, LSIS, Arts & Metiers ParisTech, 8 Blvd Louis XIV, F-59046 Lille, France

[2] INRIA Lille Nord Europe, NON A Res Team, 40 Ave Halley, F-59650 Villeneuve Dascq, France

[3] North Carolina State Univ, Edward P Fitts Dept Ind & Syst Engn, Raleigh, NC 27695 USA

来源：

NUMERICAL ALGORITHMS | 2017年 / 75卷 / 03期

关键词：

Best approximation; L-1; norm; Heaviside function; Polynomials; Polynomial splines; Chebyshev space; Weak-Chebyshev space;

D O I：

10.1007/s11075-016-0222-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the problem of best L-1 approximation of Heaviside-type functions from Chebyshev and weak-Chebyshev spaces. We extend the Hobby-Rice theorem (Proc. Am. Math. Soc., 16, 665-670, 1965) into an appropriate framework and prove the unicity of best L-1 approximation of Heaviside-type functions from an even-dimensional Chebyshev space under some assumptions on the dimension of the subspaces composed of the odd and even functions. We also apply the results to compute best L-1 approximations of Heaviside-type functions by polynomials and Hermite polynomial splines with fixed knots.

引用

页码：827 / 843

页数：17

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