Near minimax polynomial approximation
type: Item
instance of: scholarly article
title: Near minimax polynomial approximation
zbMATH Open document ID: 0912.41005
author: Maodong Ye
published in: Applied Mathematics. Series B (English Edition)
publication date: 1998-06-07T00:00:00Z
review text: Let \(f\in C^{n+1} [-1,1]\) and \(p\in P_n\) be the best approximation on \([-1,1]\) to \(f\). A near minimax approximation to \(f\in C^{n+1} [-1,1]\) is a polynomial \(p\in P_n\) satisfying \[ \| f-p\|= {1\over 2^n (n+1)!} \bigl | f(n+1) (\xi)\bigr |, \] where \(\xi\in(-1,1)\) and \(\| \cdot \|\) denotes the Chebyshev norm. In this paper the author gives a representation for linear projection and shows that the near approximation problem is equivalent to a problem of the best approximation of bivariate functions.
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 1159442
reviewed by: S. M. Mazhar
MaRDI profile type: Publication
full work available at URL: s11766-998-0015-5
OpenAlex ID: W2014708116
cites work: Q3848301
cites work: Error of truncated Chebyshev series and other near minimax polynomial approximations
cites work: The Budan-Fourier theorem for splines
cites work: Polynomial approximation using equioscillation on the extreme points of Chebyshev polynomials
DOI: 10.1007/S11766-998-0015-5
description: scientific article; zbMATH DE number 1159442