6. Quasi-Monte Carlo methods

6.1 Principles

Compared with conventional numerical analysis methods, Monte Carlo methods have the great advantage of having a convergence speed in $O\left(1\mathrm{/}\sqrt{n}\right)$ (for a sample of n points), which is independent of the problem's dimension. Nevertheless, there must be sequences of numbers that converge faster, by eliminating the random aspect. This leads to an interest in so-called quasi-Monte Carlo (QMC) methods [16].

These methods approximate