Abstract
In this work we analyze and compare the performance of an optimal stochastic approach for multidimensional integrals of smooth functions. The purpose of the present study is to compare the optimal Monte Carlo algorithm under consideration with the lattice rules based on the generalized Fibonacci numbers of the corresponding dimension and to discuss the advantages and disadvantages of each method. This is the first time this optimal stochastic approach has been compared with other stochastic approaches for mid and high dimensional integrals. The advantages and disadvantages of the stochastic approaches have been discussed.
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Acknowledgements
Venelin Todorov is supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES)”, contract No DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria and by the Bulgarian National Fund of Science under Project DN 12/5-2017 “Efficient Stochastic Methods and Algorithms for Large-Scale Computational Problems”. Stoyan Apostolov is supported by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2 - 17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics”. The work is also supported by Project KP-06-Russia/17 “New Highly Efficient Stochastic Simulation Methods and Applications” funded by National Science Fund - Bulgaria.
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Todorov, V., Apostolov, S., Dimov, I., Dimitrov, Y., Poryazov, S., Todorov, D. (2022). A Numerical Study on Optimal Monte Carlo Algorithm for Multidimensional Integrals. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. WCO 2020. Studies in Computational Intelligence, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-82397-9_24
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