Generation of New Low-Discrepancy Points
Original Publication Date: 1987-Feb-01
Included in the Prior Art Database: 2005-Jan-31
This invention provides generation of a new set of low-discrepancy points which can be easily obtained. Low-discrepancy point sets, such as Hammersley sequences and good lattice points, are very efficient for calculating approximate values of integrals of certain classes of functions defined on the multi-dimensional unit cube[*]. However, it is time-consuming to obtain these conventional low-discrepancy point sets. The new set of low-discrepancy points of this invention are based on binary vectors over GF(2). Let v(j) be a binary vector t(j1, j2, p), where j is a p-bit integer represented by (j1, j2, ..., jp) in the binary form and t( ) is a transposed matrix. v-( ) denotes a p-bit integer j, where is a binary vector t(j1, j2, ..., jp). Then a new set of points in the k-dimensional unit cube is expressed as, for j=0, 1, ...