| 基于比例移动最小二乘近似的误差分析 |
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| 引用本文： | 王青青,李小林.基于比例移动最小二乘近似的误差分析[J].应用数学和力学,2017,38(11):1289-1299. |
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| 作者姓名： | 王青青 李小林 |
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| 作者单位： | 重庆师范大学 数学科学学院, 重庆 401331 |
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| 基金项目： | 国家自然科学基金(面上项目)(11471063)，重庆市基础科学与前沿技术研究重点项目(cstc2015jcyjBX0083)，重庆市教委科学技术研究项目(KJ1600330)The National Natural Science Foundation of China (General Program)(11471063) |
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| 摘 要： | 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.
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| 关 键 词： | 无网格方法 比例移动最小二乘近似 稳定性 误差估计 |
| 收稿时间： | 2016-08-26 |
Error Analysis of the Scaled Moving Least Squares Approximation |
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| WANG Qing-qing,LI Xiao-lin.Error Analysis of the Scaled Moving Least Squares Approximation[J].Applied Mathematics and Mechanics,2017,38(11):1289-1299. |
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| Authors: | WANG Qing-qing LI Xiao-lin |
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| Institution: | School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China |
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| Abstract: | 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. |
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| Keywords: | meshless method scaled moving least squares approximation stability error estimate |
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