An upper bound of the Bézout number for piecewise algebraic curves over a rectangular partition
type: Item
instance of: scholarly article
title: An upper bound of the Bézout number for piecewise algebraic curves over a rectangular partition
zbMATH Open document ID: 1248.14064
DOI: 10.1155/2012/473582
author: Feng-Gong Lang
author: Xiao-Ping Xu
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-10-16T00:00:00Z
review text: Summary: A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces \(S^r_m(\Delta)\) and \(S^t_n(\Delta)\) over a domain \(D\) with a partition \(\Delta\), the Bézout number BN\((m, r; n, t; \Delta )\) is defined as the maximum finite number of the common intersection points of two arbitrary piecewise algebraic curves \(f(x, y) = 0\) and \(g(x, y) = 0\), where \(f(x, y) \in S^r_m(\Delta)\) and \(g(x, y) \in S^t_n(\Delta)\). In this paper, an upper bound of the Bézout number for piecewise algebraic curves over a rectangular partition is obtained.
Mathematics Subject Classification ID: 14Q10
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 6093825
zbMATH Keywords: piecewise algebraic curve
Wikidata QID: Q58704768
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/473582
OpenAlex ID: W2125059764
cites work: Q4130491
cites work: Q4143433
cites work: Q5799167
cites work: The Bézout number for piecewise algebraic curves
cites work: Estimation of the Bezout number for piecewise algebraic curve
cites work: Recent researches on multivariate spline and piecewise algebraic variety
cites work: Intersection points algorithm for piecewise algebraic curves based on Groebner bases
cites work: Isolating the real roots of the piecewise algebraic variety
cites work: Nöther-type theorem of piecewise algebraic curves
cites work: Nöther-type theorem of piecewise algebraic curves on quasi-cross-cut partition
cites work: Cayley-Bacharach theorem of piecewise algebraic curves.
DBLP publication ID: journals/ijmmsc/LangX12
description: scientific article; zbMATH DE number 6093825