An upper bound of the Bezout number for piecewise algebraic curves

被引：1
|
作者：
Wu, Jinming [1 ]
Gong, Dianxuan [2 ]
Zhang, Xiaolei [1 ]
机构：
[1] Zhejiang Gongshang Univ, Sch Math & Stat, Hangzhou 310018, Zhejiang, Peoples R China
[2] Hebei United Univ, Coll Sci, Tangshan 063009, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 273卷
基金：
中国国家自然科学基金;
关键词：
Bezout number; Piecewise algebraic curves; Homogeneous trigonometric periodic splines; Special partitions; SPLINE;
D O I：
10.1016/j.cam.2014.06.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. Based on the discussion of the number of the zeros of homogeneous trigonometric splines with different smoothness and the common points of two piecewise algebraic curves over a star partition, a better upper bound of Bezout number of two piecewise algebraic curves over arbitrary triangulation is found. Moreover, upper bounds of the Bezout number BN(m, r; n, r; Delta) for piecewise algebraic curves over several special partitions such as rectangular partition, type-1 triangulation and type-2 triangulation are obtained. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：214 / 224
页数：11
相关论文
共 19 条
  • [1] The Bezout Number of Piecewise Algebraic Curves
    Dian Xuan GONG
    Ren Hong WANG
    Acta Mathematica Sinica,English Series, 2012, (12) : 2535 - 2544
  • [2] The Bezout number of piecewise algebraic curves
    Dian Xuan Gong
    Ren Hong Wang
    Acta Mathematica Sinica, English Series, 2012, 28 : 2535 - 2544
  • [3] The Bezout number of piecewise algebraic curves
    Gong, Dian Xuan
    Wang, Ren Hong
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2012, 28 (12) : 2535 - 2544
  • [4] The Bezout number for linear piecewise algebraic curves
    Wang, Renhong
    Wang, Shaofan
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (02) : 1019 - 1030
  • [5] ESTIMATE OF THE BEZOUT NUMBER FOR LINEAR PIECEWISE ALGEBRAIC CURVES OVER ARBITRARY TRIANGULATIONS
    Wang, Shaofan
    Wang, Renhong
    Kong, Dehui
    Yin, Baocai
    SIAM JOURNAL ON DISCRETE MATHEMATICS, 2011, 25 (02) : 561 - 582
  • [6] The maximum number and its distribution of singular points for parametric piecewise algebraic curves
    Wu, Jinming
    Zhu, Chungang
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 329 : 322 - 330
  • [7] Real intersection points of piecewise algebraic curves
    Wu, Jinming
    APPLIED MATHEMATICS LETTERS, 2012, 25 (10) : 1299 - 1303
  • [8] Nother-type theorem of piecewise algebraic curves
    WANG Renhong and ZHU Chungang(Institute of Mathematical Sciences
    Progress in Natural Science, 2004, (04) : 23 - 27
  • [9] Cayley-Bacharach theorem of piecewise algebraic curves
    Wang, RH
    Zhu, CG
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 163 (01) : 269 - 276
  • [10] Nother-type theorem of piecewise algebraic curves
    Wang, RH
    Zhu, CG
    PROGRESS IN NATURAL SCIENCE-MATERIALS INTERNATIONAL, 2004, 14 (04) : 309 - 313
12