论文标题
多元线性插值和推断的一些急剧误差界
Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation
论文作者
论文摘要
我们在本文中研究了线性插值和外推的功能近似误差。呈现几个上限以及它们在尖锐的条件下。所有结果均在该函数具有Lipschitz连续梯度的假设下，并在亲密独立的样本集上插值。深度分析了二次函数的误差和双变量线性外推的误差。
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are sharp. All results are under the assumptions that the function has Lipschitz continuous gradient and is interpolated on an affinely independent sample set. Errors for quadratic functions and errors of bivariate linear extrapolation are analyzed in depth.
