AI 中文总结
本文针对规则网格数据，证明低阶移动最小二乘与多级方案的组合可改进移动最小二乘近似的收敛性，解决高阶多项式带来的高计算成本与数值不稳定性问题。
AI 中文摘要
移动最小二乘近似是从给定离散数据逼近多元函数的常用方法，为获得更高精度需使用高阶多项式，这会导致计算成本升高且出现数值不稳定性。近期，低阶移动最小二乘与多级方案的组合展现出优异的数值性能。本文将证明，在数据点构成规则网格的前提下，移动最小二乘与多级方案的这种组合确实能带来改进的收敛结果。
英文摘要
Moving least-squares approximation is a popular method for approximating multivariate functions from given discrete data. For higher accuracy higher degree polynomials have to be used, resulting also in higher computational cost and numerical instabilities. Recently, the combination of low-order moving least squares with a multilevel scheme showed superior numerical behavior. In this paper we will prove, amongst other things, that such a combination of moving least-squares with a multilevel scheme indeed leads to improved convergence results, at least if the data sites form a regular grid.
