Higher order quasi-Monte Carlo methods: A comparison
نویسندگان
چکیده
Quasi-Monte Carlo is usually employed to speed up the convergence of Monte Carlo in approximating multivariate integrals. While convergence of the Monte Carlo method is O(N−1/2), that of plain quasi-Monte Carlo can achieve O(N−1). Several methods exist to increase its convergence to O(N−α ), α > 1, if the integrand has enough smoothness. We discuss two methods: lattice rules with periodization and higher order digital nets, and present a numerical comparison.
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