Matrix computations using quasi-Monte Carlo with scrambling

Quasi-Monte Carlo methods are powerful tools for accelerating the convergence of ubiquitous MCMs. Moreover, quasi-Monte Carlo methods give smoother convergence with increasing length of the walks which is very important for computing the eigenvalues. In the same time MCMs and QMCMs have the same computational complexity. The disadvantage of quasi-Monte Carlo is the lack of practical error estimates due to the fact that the rigorous error bounds, provided via the Koksma-Hlawka are very hard to utilize. This disadvantage can be overcome by scrambling of the used sequence. Scrambling also gives a natural way to parallelize the streams. In this paper we study matrix-vector computations using scrambled sequences on the grid.