Editing Sparse grid (section)

== Curse of dimensionality ==
The standard way of representing multidimensional functions are tensor or full grids. The number of basis functions or nodes (grid points) that have to be stored and processed [[exponential function|depend exponentially]] on the number of dimensions.

The [[curse of dimensionality]] is expressed in the order of the integration error that is made by a quadrature of level <math>l</math>, with <math>N_{l}</math> points. The function has regularity <math>r</math>, i.e. is <math>r</math> times differentiable. The number of dimensions is <math>d</math>.

<math>|E_l| = O(N_l^{-\frac{r}{d}})</math>