How would you represent functions of type $[-1, 1]^n \to \mathbb R \;$ for moderate $n$? How would you integrate them?For small $n$ (1-2) such functions can be represented as histograms, vectors in some base, etc. For really large $n$ one employs other techniques, like neural networks or for integration monte-carlo methods. But what if I have to deal with $n= \overline{6 \ldots 12} \;$ ? I need to be able to compute such functions (for later integration to $\mathbb R$), but how to store, how to represent them?Having 100 points for each dimension will lead to $100^6 = 10^{12}$, whereas GiB is around $10^9$ bytes.
Working with multi-dimensional functions
high dimensional;data storage