| 两类推广的渐近迭代逼近 |
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| 引用本文： | 陈杰,王国瑾,金聪健.两类推广的渐近迭代逼近[J].自动化学报,2012,38(1):135-139. |
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| 作者姓名： | 陈杰 王国瑾 金聪健 |
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| 作者单位： | 1.浙江大学数学系计算机图象图形研究所 杭州 310027; |
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| 基金项目： | 国家自然科学基金(61070065,60933007)资助~~ |
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| 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.
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| 关 键 词： | 计算机辅助设计 渐近迭代逼近 带权渐近迭代逼近 广义严格对角占优 非标准全正基 |
| 收稿时间： | 2011-1-27 |
| 修稿时间： | 2011-5-28 |
Two Kinds of Generalized Progressive Iterative Approximations |
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| CHEN Jie,WANG Guo-Jin,JIN Cong-Jian.Two Kinds of Generalized Progressive Iterative Approximations[J].Acta Automatica Sinica,2012,38(1):135-139. |
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| Authors: | CHEN Jie WANG Guo-Jin JIN Cong-Jian |
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| Affiliation: | 1.Institute of Image Processing and Computer Graphics and the Department of Mathematics, Zhejiang University, Hangzhou 310027;2.State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027 |
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| Abstract: | In the field of computer aided design, the progressive iterative approximation (PIA) property of curves (surfaces) has wide applications in the interpolation and fitting problems, some previous works mainly discussed this PIA property in the case of normalized totally positive (NTP) basis. For general non-NTP basis, we point out that this good property also can be satisfied with some proper parameters, and many corresponding examples are given. Thus, the scope of applications of PIA can be widened. Furthermore, we discuss the convergence properties of weighted PIA with different weights, so that iterative approximation curves have different convergence rates near each data point. |
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| Keywords: | Computer aided design progressive iterative approximation weighted progressive iterative approximation generalized diagonally dominant non-normalized totally positive (non-NTP)basis |
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