三次B样条曲线插值的LUTS-PIA算法
LUTS-PIA Algorithm for Cubic B-Spline Curve Interpolation
DOI: 10.12677/AAM.2023.1210415, PDF,    科研立项经费支持
作者: 仇佩瑶, 刘仲云：长沙理工大学数学与统计学院，湖南 长沙
关键词: 曲线插值；B样条曲线；配置矩阵；LUTS分裂；渐进迭代逼近；Curve Interpolation； B-Spline Curve； Allocation Matrix； LUTS Splitting； Progressive Iterative Approximation
摘要: 本文研究了三次B样条曲线插值问题。首先，我们将配置矩阵进行下上三角分裂，然后基于该下上三角分裂提出了(Lower Upper Triangular Splitting-Progressive Iterative Approximation) LUTS-PIA算法，并证明了该算法的收敛性。最后，数值实验结果表明：LUTS-PIA算法明显优于(Hermitian and Skew-Hermitian Splitting-Progressive Iterative Approximation) HSS-PIA算法。
Abstract: The cubic B-spline curve interpolation problem is studied in this paper. First, we split the allocation matrix into lower and upper triangular parts called lower upper triangular splitting (LUTS). Based on this LUTS, we propose lower upper triangular splitting-Progressive Iterative Approximation (LUTS-PIA) algorithm and prove its convergence. Finally, we test some numerical experiments which show that LUTS-PIA has a better convergence behavior than the HSS-PIA.
文章引用：仇佩瑶, 刘仲云. 三次B样条曲线插值的LUTS-PIA算法[J]. 应用数学进展, 2023, 12(10): 4216-4223. https://doi.org/10.12677/AAM.2023.1210415

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