TY - JOUR

T1 - Parametrically splitting algorithms

AU - Ermakov, S. M.

N1 - Funding Information: ACKNOWLEDGMENTS The author thanks Yu.K. Dem’yanovich for reading the manuscript of the paper and useful comments. This work was supported by the Russian Foundation for Basic Research, project no. 08 01 00194. Copyright: Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2010/12

Y1 - 2010/12

N2 - The notion of parametrically splitting algorithms is introduced, which are characterized by their capability of solving a given problem on a large number of processors with few data transfers. These algorithms include many numerical integration algorithms, Monte Carlo and quasi-Monte Carlo methods, and so on. It is shown that parametrically splitting algorithms include, in particular, stochastic and quasi-stochastic algorithms for solving linear algebraic equations, which are particularly efficient when the number of variables is large. The parametrically splitting version of preconditioning methods is analyzed. The grid analogue of the Laplace equation in the upper relaxation method is considered in detail.

AB - The notion of parametrically splitting algorithms is introduced, which are characterized by their capability of solving a given problem on a large number of processors with few data transfers. These algorithms include many numerical integration algorithms, Monte Carlo and quasi-Monte Carlo methods, and so on. It is shown that parametrically splitting algorithms include, in particular, stochastic and quasi-stochastic algorithms for solving linear algebraic equations, which are particularly efficient when the number of variables is large. The parametrically splitting version of preconditioning methods is analyzed. The grid analogue of the Laplace equation in the upper relaxation method is considered in detail.

UR - http://www.scopus.com/inward/record.url?scp=84859725781&partnerID=8YFLogxK

U2 - 10.3103/S1063454110040047

DO - 10.3103/S1063454110040047

M3 - Article

AN - SCOPUS:84859725781

VL - 43

SP - 211

EP - 216

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -