Best linear common divisors for approximate degree reduction
type: Item
instance of: scholarly article
title: Best linear common divisors for approximate degree reduction
zbMATH Open document ID: 0772.65010
DOI: 10.1016/0010-4485(93)90041-L
published in: CAD. Computer-Aided Design
publication date: 1993-06-29T00:00:00Z
review text: Let \(f_ 1,\dots,f_ m\) be a set of polynomials of highest degree \(n\). One can search for perturbation polynomials \(\varepsilon_ j\) of degree \(\leq n\) such that \(f_ 1 + \varepsilon_ 1,\dots,f_ m + \varepsilon_ m\) have a common zero. The size of the \(m\)-vector \(\vec\varepsilon(t)\) with components \(\varepsilon_ j(t)\) is measured by the norm \(\| \vec\varepsilon\| := \max\{|\vec\varepsilon(t)|, t \in [a,b]\}\), where \(|\vec\varepsilon(t)|\) is the Euclidean norm and \([a,b]\) is a fixed interval. It is shown that this problem with the side condition that the size \(\| \vec\varepsilon\|\) of the perturbation be minimal can be solved analytically. This is applied to the problem of approximately reducing the degree of a rational curve.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 221729
zbMATH Keywords: best linear common divisors
zbMATH Keywords: minimum norm
zbMATH Keywords: rational curve
zbMATH Keywords: degree reduction
zbMATH Keywords: nearest common divisor
author: T. W. Sederberg
author: Geng-zhe Chang
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
full work available at URL: 0010-4485(93)90041-l
OpenAlex ID: W2001056482
description: scientific article; zbMATH DE number 221729