TY - JOUR

T1 - Decrease of the mean of the quasi-random integration error

AU - Ermakov, Sergei M.

AU - Leora, Svetlana N.

PY - 2019

Y1 - 2019

N2 - The article is devoted to the study of the behavior of the quasi-random integration remainder in the calculation of high-dimensional integrals. As noted in the previous work of the authors, the asymptotic behavior of its decrease, determined by the Koksma-Hlawka inequality, can be used only with a very large number of integration nodes N, which cannot be implemented on modern computers. The article introduces the concept of a mean order of decreasing remainder, which makes it possible to judge its properties with the N values available for realization and to compare various pseudo-random sequences. A number of numerical examples are given. In all cases, it turned out that the Sobol’ sequences in the sense of this criterion are somewhat better than the Holton sequences.

AB - The article is devoted to the study of the behavior of the quasi-random integration remainder in the calculation of high-dimensional integrals. As noted in the previous work of the authors, the asymptotic behavior of its decrease, determined by the Koksma-Hlawka inequality, can be used only with a very large number of integration nodes N, which cannot be implemented on modern computers. The article introduces the concept of a mean order of decreasing remainder, which makes it possible to judge its properties with the N values available for realization and to compare various pseudo-random sequences. A number of numerical examples are given. In all cases, it turned out that the Sobol’ sequences in the sense of this criterion are somewhat better than the Holton sequences.

KW - Quasi-Monte Carlo method

KW - Quasi-random sequences

KW - Randomization

UR - http://www.scopus.com/inward/record.url?scp=85067700584&partnerID=8YFLogxK

U2 - 10.1080/03610918.2019.1627370

DO - 10.1080/03610918.2019.1627370

M3 - Article

VL - 50

SP - 3581

EP - 3589

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 11

ER -