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带互异权值的渐进迭代逼近算法及其应用
  • ISSN号：1008-9497
  • 期刊名称：《浙江大学学报：理学版》
  • 时间：0
  • 分类：TP391.41[自动化与计算机技术—计算机应用技术;自动化与计算机技术—计算机科学与技术]
  • 作者机构：[1]合肥工业大学数学学院,安徽合肥230009, [2]合肥工业大学计算机与信息学院,安徽合肥230009
  • 相关基金：国家自然科学基金重点资助项目（U1135003）;国家自然科学基金资助项目（61472466,61100126）; 中国博士后科学基金面上资助项目（2015M571926）; 浙江大学CAGD＆CG国家重点实验室开放课题（A1607）
作者： 张莉[1], 赵林[1], 檀结庆[1,2]
关键词： 渐进迭代逼近, 带权渐进迭代逼近, 插值与逼近, BéZIER曲线曲面, 三角BéZIER曲面, progressive iterative approximation （PIA）, weighted progressive iterative approximation （WPIA）, interpolation and approximation, B6zier curves and surfaces, triangular Bfzier surfaces
中文摘要：

在计算机辅助几何设计（CAGD）领域,渐进迭代逼近（PIA）算法因其具有很好的自适应性和收敛稳定性,被广泛应用于插值与逼近问题.其中带权渐进迭代逼近（WPIA）算法通过调整向量加权明显加快了收敛速度.提出了一种带互异权值的渐进迭代逼近算法,不仅操作灵活,还可根据需要对各控制顶点进行调整,实现不同的迭代效果;同时通过引入一个参数,给出了可调权值迭代算法,当参数取合适值时,该算法的收敛速度比带权PIA算法更快,且权值取法不依赖于配置矩阵的特征值.最后用数值实例,通过对Bézier曲线、张量积Bézier曲面,以及三角Bézier曲面进行迭代,展示了该算法的有效性.

英文摘要：

In CAGD, progressive iterative approximation （PIA） method is widely used to solve interpolation and approximation problems due to its perfect adaptability and convergence stability. Weighted progressive iterative approximation （WPIA） can accelerate the convergence rate by assigning an appropriate weight for each adjusting vectors. One new PIA method with mutually different weights is presented. It not only provides more flexibility in operation, but also achieves satisfactory iterative result for different control vertices. A set of weights with an ad- justable parameter has also been put forward, which can be obtained without resorting to the eigenvalue of colloca- tion matrices and can speed up the convergence rate compared with the WPIA method. Numerical examples of B6zier curves, tensor-product B~zier surfaces and triangular B6zier surfaces demonstrate the effectiveness of the method.

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期刊信息
  • 《浙江大学学报：理学版》
  • 中国科技核心期刊
  • 主管单位:教育部
  • 主办单位:浙江大学
  • 主编：贺贤士 张富春
  • 地址：杭州市天目山路148号
  • 邮编：310028
  • 邮箱：zdxb_l@zju.edu.cn
  • 电话：0571-88272803
  • 国际标准刊号：ISSN：1008-9497
  • 国内统一刊号：ISSN：33-1246/N
  • 邮发代号:32-36
  • 获奖情况:
  • 第二届中国高校精品科技期刊
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国化学文摘（网络版）,美国数学评论（网络版）,英国农业与生物科学研究中心文摘,波兰哥白尼索引,德国数学文摘,荷兰文摘与引文数据库,美国剑桥科学文摘,英国动物学记录,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2014版）
  • 被引量:7855