| Autors: Stoenchev, M. R. Title: Efficient Monte Carlo algorithms for integral equations Keywords: integral equations, Monte Carlo algorithms, Fredholm integra Abstract: In this paper we propose and analyse different stochastic methods for solving a class of integral equations, namely the second kind Fredholm integral equations. We study and compare different possible approaches to compute linear functionals of the integral under consideration. Error balancing of both stochastic and systematic errors has been discussed and applied during the numerical implementation of the algorithms. An almost optimal Monte Carlo algorithm for integral equations in a combination with the idea of balancing of both systematic and stochastic errors is analysed. Conclusions about the applicability and efficiency of the algorithms have been drawn. Meaningful numerical examples and experiments with experimental and theoretical relative errors are presented. It is shown that the balancing of errors reduce the computational complexity if the error is fixed. References Issue
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Вид: публикация в международен форум, публикация в реферирано издание
