The Sparse Grids Matlab kit -- a Matlab implementation of sparse grids for high-dimensional function approximation and uncertainty quantification

The Sparse Grids Matlab Kit is a collection of Matlab functions for high-dimensional interpolation and quadrature, based on the combination technique form of sparse grids. It is lightweight, high-level and easy to use, good for quick prototyping and teaching. However, it has some features that allow its use also in realistic applications: in particular, the Sparse Grids Matlab Kit is somehow geared towards Uncertainty Quantification, but it is flexible enough for other purposes. The goal of this paper is to provide an overview of the data structure and of mathematical aspects forming the backbone of the software, as well as to compare it with similar software available in literature.