Sparse Grids in a Nutshell

摘要

The technique of sparse grids allows to overcome the curse of dimensionality, which prevents the use of classical numerical discretization schemes in more than three or four dimensions, under suitable regularity assumptions. The approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This entry level article gives an introduction to sparse grids and the sparse grid combination technique.