Universal modification of vector weighted method of correlated sampling with finite computational cost

• Published in: Russian journal of numerical analysis and mathematical modelling Vol. 34; no. 1; pp. 43 - 55
• Main Author: Medvedev, Ilya N.
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.02.2019; Walter de Gruyter GmbH
• Subjects: 65C05; Algorithms; branching of Markov chain trajectory; Chain branching; Computational efficiency; Construction costs; finite computational cost; Integral equations; Markov analysis; Markov chains; matrix weight, weighted method of correlated sampling; Sampling; System of linear integral equations of the second kind; transfer of polarized radiation; vector weighted estimator
• ISSN: 0927-6467; 1569-3988
• DOI: 10.1515/rnam-2019-0004

The weighted method of dependent trials or weighted method of correlated sampling (MCS) allows one to construct estimators for functionals based on the same Markov chain simultaneously for a given range of the problem parameters. Choosing an appropriate Markov chain, it is necessary to take into account additional conditions providing the finiteness of the computational cost of weighted MCS. In this paper we study the issue of finite computational cost of the method of correlated sampling (MCS) in application to evaluation of linear functionals of solutions to a set of systems of 2nd kind integral equations. A universal modification of the vector weighted MCS is constructed providing the branching of chain trajectory according to elements of matrix weights. It is proved that the computational cost of the constructed algorithm is bounded in the case the base functionals are also bounded. The results of numerical experiments using the modified weighted estimator are presented for some problems of the theory of radiation transfer subject to polarization.