Inverse rational \(L^ 1\) approximation
type: Item
instance of: scholarly article
title: Inverse rational \(L^ 1\) approximation
zbMATH Open document ID: 0846.41015
author: R. C. Gayle
published in: Journal of Approximation Theory
publication date: 1996-09-10T00:00:00Z
review text: Considering the nonlinear approximating family \(\mathbb{R}^n_m\) of rational expressions over a given interval, the author studies the question as to which elements of the family may arise as best approximation to continuous functions from outside the family. It is shown that there exist continuous functions not in the above family which do have any given defect on functions, as their best \(L^1\) approximation [cf. \textit{C. B. Dunham}, J. Approximation Theory 4, 269-273 (1971; Zbl 0217.42501)]. Variational techniques from \textit{J. M. Wolfe} [J. Approximation Theory 17, 166-176 (1976; Zbl 0373.41025)] are used for the proof.
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 810859
zbMATH Keywords: rational \(L^ 1\) approximation
zbMATH Keywords: best approximation
zbMATH Keywords: continuous functions
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: jath.1995.1109
OpenAlex ID: W1970710225
DOI: 10.1006/JATH.1995.1109
description: scientific article; zbMATH DE number 810859