Abstract
We perform computational investigations to compare the performance of Latin hypercube sampling (LHS method) and a particular QMC lattice rule based on generalized Fibonacci numbers (FIBO method) for integration of smooth functions of various dimensions. The two methods have not been compared before and both are generally recommended in case of smooth integrands. The numerical results suggests that the FIBO method is better than LHS method for low-dimensional integrals, while LHS outperforms FIBO when the integrand dimension is higher. The Sobol nets, which performence is given as a reference, are outperformed by at least one of the two discussed methods, in any of the considered examples.
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Acknowledgements
This work was supported by the Program for career development of young scientists, BAS, Grant No. DFNP-91/04.05.2016, by the Bulgarian National Science Fund under grant DFNI I02-20/2014, and the financial funds allocated to the Sofia University St. Kl. Ohridski, grant No. 197/2016.
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Dimitrov, S., Dimov, I., Todorov, V. (2017). Latin Hypercube Sampling and Fibonacci Based Lattice Method Comparison for Computation of Multidimensional Integrals. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_32
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DOI: https://doi.org/10.1007/978-3-319-57099-0_32
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