COMPUTING HIGH DIMENSIONAL INTEGRALS WITH MONTE CARLO METHODS

COMPUTING HIGH DIMENSIONAL INTEGRALS WITH MONTE CARLO METHODS

Authors

  • Venelin Todorov Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG

DOI:

https://doi.org/10.46687/jsar.v10i1.200

Keywords:

Monte Carlo and quasi Monte Carlo algorithms, multidimensional integrals, quasi Monte Carlo algorithm based on Sobol sequence, plain Monte Carlo algorithm

Abstract

High dimensional integrals are usually solved with Monte Carlo algorithms and quasi Monte Carlo algorithms. We are doing numerical testing which compare low discrepancy and Monte Carlo algorithms. It is well known that Sobol algorithm has some advantageous over the other low discrepancy sequences, that’s why we use this algorithm for our numerical example. The obtained relative error confirms this superiority of the presented Monte Carlo and quasi Monte Carlo algorithms even when small number of sample points are used. It is very interesting that the presented high dimensional integral gives very low relative error even for computational time less than one second which shows the great importance of the developed algorithms.

Author Biography

Venelin Todorov , Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG

Bulgarian Academy of Sciences, Institute of Mathematics and Informatics and Institute of Inormation and Communication Technologies: Sofia, BG

ORCID iD icon https://orcid.org/0000-0001-7134-5901

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Published

18.03.2023

How to Cite

Todorov , V. . (2023). COMPUTING HIGH DIMENSIONAL INTEGRALS WITH MONTE CARLO METHODS: COMPUTING HIGH DIMENSIONAL INTEGRALS WITH MONTE CARLO METHODS. JOURNAL SCIENTIFIC AND APPLIED RESEARCH, 10(1), 11–16. https://doi.org/10.46687/jsar.v10i1.200

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