Investigation of methods of numerical integration with optimal convergence speed

E.G. Kablukova
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E.G. Kablukova: Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Lavrentyeva 6, Novosibirsk, 630090, Russia; e-mail: Jane_K@ngs.ru.

Monte Carlo Methods and Applications, 2005, vol. 11, issue 4, 397-406

Abstract: The comparison of optimal algorithms in functional Bachvalov classes with special importance sampling technique and simplest stochastic and deterministic methods of numerical integration is presented. This comparison was provided with the help of stochastic test system, which uses the samples of spectral models of random fields. The advantages of this system (in particular, the possibilities of getting functions of needed class and estimates of mean error) are shown. The cases, when the effectiveness of theoretically optimal algorithms is not higher compared with the importance sampling technique and methods of numerical integration, are discovered.

Date: 2005
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DOI: 10.1515/156939605777438587

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