Remarks on randomization of quasi-random numbers - Ermakov, Sergej M.; Leora, Svetlana N. (Monte Carlo methods and applications, 2018)
In this paper we discuss estimation of the quasi-Monte Carlo methods error in the case of calculation of high-order integrals. Quasi-random Halton sequences are considered as a special case. Randomization of these sequences by the random shift method turns out to lead to well-known random quadrature formulas with one free node. Some new properties of such formulas are pointed out. The subject is illustrated by a number of numerical examples.