文章基本信息

标题：An Upper Bound of the Bezout Number for Piecewise Algebraic Curves over a Rectangular Partition
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作者：Feng-Gong Lang ; Xiao-Ping Xu
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2012
卷号：2012
DOI：10.1155/2012/473582
出版社：Hindawi Publishing Corporation
摘要：A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces 𝑆𝑟𝑚 (Δ) and 𝑆𝑡𝑛 (Δ) over a domain D with a partition Δ, the Bezout number BN(m,r;n,t;Δ) 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)∈𝑆𝑟𝑚 (Δ) and 𝑔(𝑥,𝑦)∈𝑆𝑡𝑛 (Δ). In this paper, an upper bound of the Bezout number for piecewise algebraic curves over a rectangular partition is obtained.