TY - JOUR

T1 - The Monte-Carlo algorithm for the solving of systems of linear algebraic equations by the Seidel method

AU - Tovstik, T. M.

AU - Volosenko, K. S.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - The iteration algorithm is used to solve systems of linear algebraic equations by the Monte-Carlo method. Each next iteration is simulated as a random vector such that its expectation coincides with the Seidel approximation of the iteration process. We deduce a system of linear equations such that mutual correlations of components of the limit vector and correlations of two iterations satisfy them. We prove that limit dispersions of the random vector of solutions of the system exist and are finite.

AB - The iteration algorithm is used to solve systems of linear algebraic equations by the Monte-Carlo method. Each next iteration is simulated as a random vector such that its expectation coincides with the Seidel approximation of the iteration process. We deduce a system of linear equations such that mutual correlations of components of the limit vector and correlations of two iterations satisfy them. We prove that limit dispersions of the random vector of solutions of the system exist and are finite.

KW - system of linear algebraic equations

KW - the Monte-Carlo method

KW - the Seidel algorithm

UR - http://www.scopus.com/inward/record.url?scp=84991013870&partnerID=8YFLogxK

U2 - 10.3103/S1063454116030122

DO - 10.3103/S1063454116030122

M3 - Article

AN - SCOPUS:84991013870

VL - 49

SP - 269

EP - 276

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -