We discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor's formula monomial basis. Error bounds for the approximation of partial derivatives of any order compatible with the function regularity are provided, as well as sensitivity estimates to functional perturbations, in terms of the inverse Vandermonde coefficients that are active in the differentiation process. Several numerical tests are presented showing the accuracy of the approximation.

翻译：我们讨论基于Discrete Leja Point点当地多元内插系数、以泰勒公式单数为基础的多变量分散数据的点数数字区分公式,提供符合功能正常性的任何订单部分衍生物近似值的错误界限,以及功能扰动的敏感估计值,说明在差异化过程中活跃的Vandermonde系数的反向。