基于泰勒基函数的移动最小二乘法及误差分析  

THE MOVING LEAST SQUARE BASED ON TAYLOR BASIS & ERROR ANALYSIS

作　　者：袁占斌[1] 聂玉峰[1] 欧阳洁[1] 

机构地区：[1]西北工业大学理学院数学系,西安710072

出　　处：《数值计算与计算机应用》2012年第1期25-31,共7页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11071196);校基础研究基金

摘　　要：移动最小二乘法通常选用不超过m次单项式生成基函数空间,本文选用了以计算点(?)为平移点的泰勒基函数生成基空间.理论和数值试验发现:选用此种基函数后会降低形函数及导数计算的复杂性,并且有效减小广义逆矩阵的条件数,提高了计算效率同时增加了计算稳定性,并用该方法推导出移动最小二乘近似的收敛阶及误差主部.In moving least squares approximation, the often-used basis functions are monomials not higher than m-th order. In this paper a new type of function named Taylor basis function is used to construct the basis space. Through theory analysis and numerical test, we find it is easier to compute the shape function and differential function after this modification, at the same time the condition number of generalized inverse matrix is lower than that generated by monomial basis. In a word this modification can improve the computational efficiency and stability, another benefit is to analysis the error of approximation easily.

关 键 词：无网格方法 移动最小二乘法 泰勒基函数 误差分析 

分 类 号：O241.5[理学—计算数学]