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的稀疏网格线性算法在无权重或加权Sobolev混合光滑函数近似恢复与积分问题中的最新成果，并将部分结果推广至更一般情形。