Quasi Monte Carlo integration algorithm with a posteriori error analysis

Authors

  • Anton A. Antonov St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;

Abstract

A possibility of a probabilistic approach to a deterministic error estimation procedure of quasi Monte-Carlo method is presented. Existing estimation methods of the aforementioned estimation are non-constructive. A previously obtained result, which was deduced from the theory of random cubature formulae, is expanded with new theoretical results. Qint algorithm, which is presented in a convenient for direct application step-by-step form, is discussed in terms of parametrization. Several key features of Qint are discussed, including monotonicity by a partition parameter and accuracy dependency on a partition rule. New practical results are presented, which are obtained with the help of Sobol sequences and TESTPACK integrand functions. In all cases a better estimate compared to a traditional Monte Carlo confidence interval is demonstrated. Refs 14. Figs 4.

Keywords:

Monte Carlo and quasi Monte Carlo method, confidence interval, random cubature formulae, Haar functions, Sobol sequences

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Published

2015-02-01

How to Cite

Antonov, A. A. (2015). Quasi Monte Carlo integration algorithm with a posteriori error analysis. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(1), 3–13. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11103

Issue

Vol. 2 No. 1 (2015)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.