空间曲线的拟插值重建  

QUASI-INTERPOLATION RECONSTRUCTION FOR SPACE CURVES

作　　者：刘新儒[1,2] 任燕 王海波 刘圣军[1,2] Liu Xinru;Ren Yan;Wang Haibo;Liu Shengjun(School of Mathematics and Statistics,Central South University,Changsha 410083,China;Institute of Engineering Modeling and Scientific Computing,Central South University,Changsha 410083,China;Chongqing Mechanical Senior Technician School,Chongqing 400055,China)

机构地区：[1]中南大学数学与统计学院,长沙410083 [2]中南大学工程建模与科学计算研究所,长沙410083 [3]重庆市机械高级技工学校,重庆400055

出　　处：《数值计算与计算机应用》2023年第1期68-80,共13页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(62172447)资助.

摘　　要：在一元Multiquadric拟插值算子的基础上,将一元基函数扩展到多元,并重新定义了空间点之间的距离,提出了一种新的多元拟插值算子,并分析了其任意阶多项式再生性及逼近性.数值实验表明,新的多元拟插值算子可直接使用空间点集的坐标实现曲线的高精度拟插值重建.Based on the univariate multiquadric quasi-interpolation operator,the univariate basis function is extended to multivariate basis function,and the distance between spatial points is redefined,and a new multivariate quasi-interpolation operator is proposed.We analyzed any degree polynomial reproduction property and the approximation of the quasi-interpolation operator.Numerical experiments showed that the new multivariate quasi-interpolation operator can achieve high-precision quasi-interpolation reconstruction of the space curve by using the coordinates of the spatial point set directly.

关 键 词：拟插值 空间曲线 Multiquadric(MQ) 多项式再生性 

分 类 号：O241.3[理学—计算数学]