We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite set. Some of them are extended to more general cases.

翻译：本文简要综述了基于有限采样点值、具有无权重或加权的Sobolev混合光滑性函数的稀疏网格线性近似恢复与积分算法的最新结果，并将部分结论推广至更一般情形。