Higher Order Quasi-Monte Carlo Methods: A Comparison | Zendy

Dirk Nuyens | Zendy; Ronald Cools | Zendy; Theodore E. Simos | Zendy; George Psihoyios | Zendy; Ch. Tsitouras | Zendy

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Higher Order Quasi-Monte Carlo Methods: A Comparison

Author(s) -

Dirk Nuyens,

Ronald Cools,

Theodore E. Simos,

George Psihoyios,

Ch. Tsitouras

Publication year - 2010

Publication title -

aip conference proceedings

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.177

H-Index - 75

eISSN - 1551-7616

pISSN - 0094-243X

DOI - 10.1063/1.3498535

Subject(s) - monte carlo method , computer science , statistical physics , mathematics , physics , statistics

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 near O(N−1). Several methods exist to increase its convergence to near 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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