The Derandomization Of Halton Sequences In Quasi-Monte Carlo

As we know,a drawback of MC methods is their low convergence,O(N^-1/2),Onegeneric approach to improving the convergence of MC methods has been the use ofhighly uniform random numbers in place of the usual pseudorandom numbers,calledQuasi-Monte Carlo methods.we only obtain the theoretical supper boundary ,itcannot o?er statistical error estimates .To employ the independence of MC andthe uniformity of QMC,randomized quasi-Monte Carlo (RQMC)methods is recentlyproposed .RQMC maintain the convergence of QMC and offer error estimates andproduce a family of quasi-Monte Carlo sequences .a natural question is how to choosean optimal quasirandom sequence from this family.The process of finding an optimalquasirandom sequences is called the derandomization of a randomized family.In thispaper ,we use the linear scrambling method to random the Halton sequence,andemploy the discrepancy criteria to choose the optimal Halton sequence.