【摘要】 已知的基于移动最小二乘法(MLS)的数据拟合存在较大的提升空间,提出了一种改进的移动最小二乘法(IMLS)。通过对正态加权函数与两种典型加权函数的分析与对比,证明了正态加权优越的拟合性能。以正态加权作为加权函数对移动最小二乘法进行了改进,并对其影响半径与形状参数对拟合性能的影响进行了深入研究,给出了曲线拟合和曲面拟合的数值实例,数值算例和测量数据处理表明,改进的移动最小二乘法在曲线拟合和曲面构造方面性能优于移动最小二乘。更多还原

【Abstract】 The known data fitting based on moving least squares(MLS) has a large lifting space, this paper proposes an improved moving least squares(IMLS). Through the analysis and comparison of the normal weighting function and two typical weighting functions, the superior fitting performance of the normal weighting is proved. The moving least square method is improved by taking the normal weighting as the weighting function, and the influence of its influence radius and shape parameter on the fitting performance is deeply studied, numerical examples of curve fitting and surface fitting are given, numerical examples and measurement data processing show that the improved moving least square method is superior to the moving least square method in curve fitting and surface construction.更多还原