TY - JOUR

T1 - Universal modification of vector weighted method of correlated sampling with finite computational cost

AU - Medvedev, Ilya N.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - 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.

AB - 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.

KW - branching of Markov chain trajectory

KW - fnite computational cost

KW - matrix weight

KW - System of linear integral equations of the second kind

KW - transfer of polarized radiation

KW - vector weighted estimator

KW - weighted method of correlated sampling

UR - http://www.scopus.com/inward/record.url?scp=85061426926&partnerID=8YFLogxK

U2 - 10.1515/rnam-2019-0004

DO - 10.1515/rnam-2019-0004

M3 - Article

AN - SCOPUS:85061426926

VL - 34

SP - 43

EP - 55

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 1

ER -