文档介绍：散乱数据曲面拟合的局部加权最小二乘插值方法及权函数的选择讨论
刘福保,李卫国
1. 长沙民政职业技术学院文法系
2. 南京航空航天大学机电学院
摘要:本文首先用局部加权最小二乘法将三维空间内任意散乱数据点集均匀,再估计出立方体网格点上的偏导数值及混合偏导数值,最后仅用网格点数据进行快速光滑插值加密计算,从而可得到任意点处的函数值。通过对已知函数的随机数据点集进行计算,取得了令人满意的效果。同时,在最小二乘逼近过程中,本文提供了一种权函数,并与其它二种权函数进行分析比较,给出了各种情况下的误差。
关键词:散乱数据,最小二乘,权函数,插值
The Topic on Choice of Weighted Functional and Local Weighted Least-mean Square Method for Surface Interpolation to Scattered Data
Fubao ,CHangSha scoclal work collgeg ,ChangSha,410004,China
2. Li Weiguo , Nanjing University of Aeronautics & Astronautics(南航),    College of Mechanical and Electrical Engineering(机电学院), Nanjing 210016, China
Abstract: In this article, a uniform grid data is firstly sampled from the scattered data in 3D space by local weighted least square mean method, then partial and mixed partial derivative value on the volume grid node position is estimated, finally the grid data are interpolated to be a global functional by smoothing and densification a prior. We reported some satisfactory case results at the end of this article. Also, in the process of least square mean fitting, a best weighted functional was adopted pared with other two traditional weighted functional. We also presented the error in the case of varied inputted parameters.
Keywords: scattered data, least square mean, weighted functional, interpolation
1、引言
给定平面区域内的某一散乱点集D=以及对应点上的函数值,求一个二元函数使其满足(),这就是三维空间内散乱