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A. V. Voytishek, V. V. Shvets

Complete optimization of a discrete stochastic numerical procedure for globally estimating the solution of an integral equation of the second kind

In this paper we study an algorithm for estimating the solution of an integral second-kind equation by values at mesh nodes which are obtained using a local estimate of the Monte Carlo method. We consider a complete optimization problem in which, in addition to the number of mesh nodes and the number of trajectories selected in the Monte Carlo method, we select an optimum transition density specifying a corresponding Markov chain. This density is chosen from a class of piecewise constant approximations of optimal density in the dependent test method in the space L ₂(V).

Russian Journal of Numerical Analysis and Mathematical Modelling, Walter de Gruyter

Print ISSN: 0927-6467
Volume: 21, 05/2006
Pages: 251 - 267

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