The Initialization of Sobol Numbers
To construct a Sobol sequence a set of direction numbers vi,j needs to be selected. There is some freedom in the selection of initial direction numbers. Therefore, it is possible to receive different realisations of the Sobol sequence for selected dimensions. A bad selection of initial numbers can considerably reduce the efficiency of Sobol sequences when used for computation.
Arguably the easiest choice for the initialisation numbers is just to have the l-th leftmost bit set, and all other bits to be zero, i.e. mk,j = 1 for all k and j. This initialisation is usually called unit initialisation. However, such a sequence fails the test for Property A and A’ even for low dimensions and hence this initialisation is bad.
Read more about this topic: Sobol Sequence
Famous quotes containing the word numbers:
“... there are persons who seem to have overcome obstacles and by character and perseverance to have risen to the top. But we have no record of the numbers of able persons who fall by the wayside, persons who, with enough encouragement and opportunity, might make great contributions.”
—Mary Barnett Gilson (1877–?)