Tag Archives: tiling

Quasi-Monte Carlo for R^s: digital nets and worst-case error

Recently I submitted the paper titled Quasi-Monte Carlo numerical integration over $\mathbb{R}^s$: digital nets and worst-case error. I will give some heuristic explanation of the results in this paper. Interesting in this context is also the sparse grid approach from the PhD thesis of Markus Holtz (supervised by Prof. Michael Griebel).

Therein I aim to develop a theory on quasi-Monte Carlo integration over $\mathbb{R}^s$. The idea is to transform a digital net from $[0,1]^s$ to $\mathbb{R}^s$ such that in elementary intervals of the form $\displaystyle \prod_{i=1}^s [A b^j, (A+1) b^j)$ one has a digitally shifted digital net, and at the same time, globally one has a given (discretized) distribution. Continue reading