Methods for bounding the range of a polynomial
type: Item
instance of: scholarly article
title: Methods for bounding the range of a polynomial
zbMATH Open document ID: 0833.65011
DOI: 10.1016/0377-0427(93)E0270-V
author: Qun Lin
author: J. Rokne
published in: Journal of Computational and Applied Mathematics
publication date: 1996-03-14T00:00:00Z
review text: Let \(p(x)= \sum_{s=0}^n a_s x^s\) be a real polynomial. Then bounds of \(p(x)\) over the interval \([0, 1]\) are determined as follows: Let \(A_j (x)\), \(j\in J\), be nonnegative basis functions with a finite index set \(J\), such that \(\sum_{j\in J} A_j (x)=1\) and \(x^s= \sum_{j\in J} \mu_{js} A_j (x)\) for \(s=0, \dots, n\) and appropriate coefficients \(\mu_{js}\). Then \(\min_{j\in J} \xi_j\) and \(\max_{j\in J} \xi_j\) are a lower and an upper bound, respectively. -- Practical applications arise at the development of polynomials by Bernstein polynomials and by \(B\)-splines.
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 804736
zbMATH Keywords: range of a polynomial
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: \(B\)-splines
reviewed by: H. Ratschek
MaRDI profile type: Publication
cites work: Bernstein form of a polynomial
cites work: On calculating with B-splines
cites work: Bounds on a polynomial
cites work: Q3707258
cites work: Bounds for an interval polynomial
full work available at URL: 0377-0427(93)e0270-v
OpenAlex ID: W2033403483
description: scientific article; zbMATH DE number 804736