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两类推广的渐近迭代逼近

陈杰 王国瑾 金聪健

陈杰, 王国瑾, 金聪健. 两类推广的渐近迭代逼近. 自动化学报, 2012, 38(1): 135-139. doi: 10.3724/SP.J.1004.2012.00135
引用本文: 陈杰, 王国瑾, 金聪健. 两类推广的渐近迭代逼近. 自动化学报, 2012, 38(1): 135-139. doi: 10.3724/SP.J.1004.2012.00135
CHEN Jie, WANG Guo-Jin, JIN Cong-Jian. Two Kinds of Generalized Progressive Iterative Approximations. ACTA AUTOMATICA SINICA, 2012, 38(1): 135-139. doi: 10.3724/SP.J.1004.2012.00135
Citation: CHEN Jie, WANG Guo-Jin, JIN Cong-Jian. Two Kinds of Generalized Progressive Iterative Approximations. ACTA AUTOMATICA SINICA, 2012, 38(1): 135-139. doi: 10.3724/SP.J.1004.2012.00135

两类推广的渐近迭代逼近

doi: 10.3724/SP.J.1004.2012.00135
详细信息
    通讯作者:

    王国瑾浙江大学数学系教授.主要研究方向为计算机辅助几何设计和应用逼近论.本文通信作者.E-mail: wanggj@zju.edu.cn

Two Kinds of Generalized Progressive Iterative Approximations

  • 摘要: 在计算机辅助设计领域里,曲线或曲面的渐近迭代逼近(Progressive iterative approximation,PIA)性质在插值与拟合问题中有着广泛的应用,以前的文献对这一性质的讨论主要局限在标准全正基的情形.对于一般的非标准全正基,本文指出,其在适当的参数下也有可能同样具有这一优良的性质,并给出了相应的实例,从而拓宽了渐近迭代逼近的适用范围.与此同时,还讨论了权因子各不相同时,带权渐近迭代逼近的收敛性,使得迭代逼近曲线对不同的控制顶点,具有不同的加速收敛速度.
  • [1] Qi D,Tian Z,Zhang Y,Feng J. The method of numeric polish in curve fitting. Acta Mathematica Sinica,1975,18(3):173-184[2] Boor C D. How does Agee's smoothing method work? [Online],available:ftp://ftp.cs.wisc.edu/Approx/agee.pdf,July 24,2011[3] Lin H W,Wang G J,Dong C S. Constructing iterative non-uniform B-spline curve and surface to fit data points. Science in China Series F:Information Sciences,2004,47(3):315-331[4] Lin H W,Bao H J,Wang G J. Totally positive bases and progressive iteration approximation. Computers and Mathematics with Applications,2005,50(3-4):575-586[5] Delgado J,Peoa J M. Progressive iterative approximation and bases with the fastest convergence rates. Computer Aided Geometric Design,2007,24(1):10-18[6] Delgado J,Peoa J M. On the generalized Ball bases. Advances in Computational Mathematics,2006,24(1-4):263-280[7] Ando T. Totally positive matrices. Linear Algebra and Its Applications,1987,90:165-219[8] Karlin S. Total Positivity. Stanford:Stanford University Press,1968[9] Lu L Z. Weighted progressive iteration approximation and convergence analysis. Computer Aided Geometric Design,2010,27(2):129-137[10] Lin H W. Local progressive-iterative approximation format for blending curves and patches. Computer Aided Geometric Design,2010,27(4):322-339[11] Delgado J,Peoa J M. A comparison of different progressive iteration approximation methods. Mathematical Methods for Curves and Surfaces,2010,5862:136-152[12] Lin H W. The convergence of the geometric interpolation algorithm. Computer-Aided Design,2010,42(6):505-508[13] Horn R A,Johnson C R. Matrix Analysis. Beijing:China Machine Press,2005[14] Wang Guo-Jin,Wang Guo-Zhao,Zheng Jian-Min. Computer Aided Geometric Design. Beijing:Higher Education Press,2001(王国瑾,汪国昭,郑建民. 计算机辅助几何设计. 北京:高等教育出版社,2001)[15] Wang Song-Gui,Jia Zhong-Zhen. Inequalities in Matrix Theory. Hefei:Anhui Education Press,1994(王松桂,贾忠贞. 矩阵论中不等式. 合肥:安徽教育出版社,1994)
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出版历程
  • 收稿日期:  2011-01-27
  • 修回日期:  2011-05-28
  • 刊出日期:  2012-01-20

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