基于比例移动最小二乘近似的误差分析

Error Analysis of the Scaled Moving Least Squares Approximation

相较于移动最小二乘近似方法,比例移动最小二乘近似法有效地克服了前者带来的矩阵病态这一问题,展示出了更好的数值稳定性和更高的计算精度.给出了比例移动最小二乘近似对函数及其任意阶导数的误差估计,并给出了数值算例来验证之前的理论分析结果,通过与移动最小二乘近似的比较,表明比例移动最小二乘近似能得到更快的收敛性和更稳定的计算性.

Compared with the moving least squares（MLS） approximation,the scaled moving least squares（SMLS） approximation can avoid the issue of ill-conditioned matrices involved in the MLS approximation. Error estimates of the SMLS approximation were conducted for the approximation function and its arbitrary-order derivatives. Finally,some numerical examples were given. The numerical results indicate that the SMLS approximation provides monotonic convergence and higher accuracy with higher computational stability in comparison with the MLS approximation.