On the numerical condition of polynomials in Bernstein form
type: Item
instance of: scholarly article
title: On the numerical condition of polynomials in Bernstein form
zbMATH Open document ID: 0636.65012
DOI: 10.1016/0167-8396(87)90012-4
author: V. T. Rajan
author: Rida T. Farouki
published in: Computer Aided Geometric Design
publication date: 1987-01-01T00:00:00Z
review text: The Bernstein-Bézier curve and surface forms play an important part in approximation theory and computer aided design. From the point of view of condition numbers of polynomials, the authors discuss the advantages of the polynomials in Bernstein form over the polynomial in other forms. Generally speaking, the authors prove the following fact that, among a large family of polynomial bases, the Bernstein basis shows optimal root conditioning. At last, some examples are used to illustrate these results.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 4037016
zbMATH Keywords: Bernstein-Bézier curve and surface forms
zbMATH Keywords: computer aided design
zbMATH Keywords: condition numbers of polynomials
zbMATH Keywords: Bernstein basis
zbMATH Keywords: optimal root conditioning
MaRDI profile type: Publication
full work available at URL: 0167-8396(87)90012-4
OpenAlex ID: W1998916693
cites work: Q5665063
cites work: Q5539920
cites work: A survey of curve and surface methods in CAGD
cites work: Bernstein form of a polynomial
cites work: Q3848301
cites work: The characterization of parametric surface sections
cites work: Interactive Interpolation and Approximation by Bezier Polynomials
cites work: The Condition of Orthogonal Polynomials
cites work: On the condition of algebraic equations
cites work: The Condition of Polynomials in Power Form
cites work: Q3707259
cites work: Markov chains and computer-aided geometric design: part I - problems and constraints
cites work: Polya’s Urn Model and Computer Aided Geometric Design
cites work: Bernstein-Bézier Methods for the Computer-Aided Design of Free-Form Curves and Surfaces
cites work: Principles for Testing Polynomial Zerofinding Programs
cites work: Q5585021
cites work: A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
cites work: Bounds on a polynomial
cites work: Q5819609
cites work: Stable evaluation of polynomials
cites work: Q5829318
cites work: Practical Problems Arising in the Solution of Polynomial Equations
cites work: Q3992847
cites work: Bounds for the Horner Sums
cites work: On the conditioning of polynomial and rational forms
cites work: A Theory of Condition
cites work: Some new characterizations of the Chebyshev polynomials
cites work: Q5558053
cites work: On the Problem of Runs
cites work: The evaluation of the zeros of ill-conditioned polynomials. I, II
cites work: Error analysis of floating-point computation
cites work: Q4871634
description: scientific article; zbMATH DE number 4037016