修正的移动最小二乘方法

Modified Moving Least Square Method

摘要: 本文在MLH (Moving Least-Hardy)逼近方法的基础上，通过在MLS (Moving Least-Squares)方法中引入修正权给出了一种修正的MLS方法。该方法与MLH方法一样，能够对带有奇异值的散乱数据进行有效的逼近，避免了MLS方法对这类数据逼近的不理想问题，并且其计算效率明显高于MLS方法。为了提高逼近值精度，该方法还引入了自然邻点，以自然邻点替代目标函数中权函数的作用。

Abstract: In this paper, based on the MLH (Least-Hardy Moving) method, we present a modified MLS (Moving Least-Squares) method by introducing the correction weight in MLS method. The method is the same as the MLH method, which can effectively approximate the scattered data with outliers. At the same time, this method avoids the problem of MLS method to approximate this kind of scattered data, and its computing efficiency is significantly better than that of MLH method. In order to improve the accuracy of approximation, we also introduce the natural neighbor points, which replace the role of MLS weight function.