A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy
This work provides a more efficient construction method for practitioners using quasi-Monte Carlo methods with weighted spaces.
The paper reduces the construction cost of polynomial lattice point sets for quasi-Monte Carlo integration by restricting the polynomial selection set, leveraging fast-decaying weights to maintain low weighted star discrepancy.
The weighted star discrepancy is a quantitative measure for the performance of point sets in quasi-Monte Carlo algorithms for numerical integration. We consider polynomial lattice point sets, whose generating vectors can be obtained by a component-by-component construction to ensure a small weighted star discre-pancy. Our aim is to significantly reduce the construction cost of such generating vectors by restricting the size of the set of polynomials from which we select the components of the vectors. To gain this reduction we exploit the fact that the weights of the spaces we consider decay very fast.