On the unicity of best \(L_ 1\)-approximation by polynomials of several variables
type: Item
instance of: scholarly article
title: On the unicity of best \(L_ 1\)-approximation by polynomials of several variables
zbMATH Open document ID: 0549.41018
DOI: 10.1007/BF01956778
published in: Acta Mathematica Hungarica
publication date: 1983-01-01T00:00:00Z
review text: The problem of best \(L_ 1\)-approximation by polynomials of several variables for continuous rational functions on an open bounded connected subset K of \({\mathbb{R}}^ n\) is studied and the uniqueness of the approximation is proved. The author comments that the method of the paper is unlikely to give a solution to the corresponding problem for an element of the general subspace C(K). The main theorem of the paper is used to verify the uniqueness of the solutions on a rectangular region of a Korkin-Zolotarjov type extremal problem for polynomials of several variables and the explicit solution presented.
Mathematics Subject Classification ID: 41A52
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 3875928
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Haar subspaces
zbMATH Keywords: relatively prime polynomials
zbMATH Keywords: best \(L_ 1\)-approximation
zbMATH Keywords: Korkin-Zolotarjov type extremal problem
author: András Kroó
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
cites work: Some theorems on unicity of multivariateL 1-approximation
cites work: Some theorems on Cebysev approximation. II
cites work: Q5595759
cites work: Chebyshev polynomials of several variables
full work available at URL: https://doi.org/10.1007/bf01956778
OpenAlex ID: W2002661777
description: scientific article; zbMATH DE number 3875928