Optimal recovery of multivariate functions restricted by second-order differential operator
Optimal recovery of multivariate functions restricted by second-order differential operator
复制标题
二阶微分算子限制多元函数的最优恢复
作者：
谷懿;刘永平
我们考虑R^d中凸体上的函数类，它们在任何方向上都被某个二阶微分算子一致有界，以及关于满秩格L的周期函数类，它们在任何方向上都有相同的限制。我们研究了这些类的最优恢复问题，并得到了最优算法的估计，恢复功能，其值和梯度值在n个节点，分别。
We consider the class of functions on a convex body in R^d , which are uniformly bounded by some second-order differential operator in any direction, and the class of periodic functions with respect to a full-rank lattice L, which have the same restriction in any direction. We study the optimal recovery problems of these classes and obtain the estimate of the optimal algorithm that recovers functions with their values and gradient values at n nodes, respectively.