Abstract
In this paper we develop stochastic simulation methods for solving large systems of linear equations, and focus on two issues: (1) construction of global random walk algorithms (GRW), in particular, for solving systems of elliptic equations on a grid, and (2) development of local stochastic algorithms based on transforms to balanced transition matrix. The GRW method calculates the solution in any desired family of prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman–Kac formula. The use in local random walk methods of balanced transition matrices considerably decreases the variance of the random estimators and hence decreases the computational cost in comparison with the conventional random walk on grids algorithms.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 20-51-18009
Funding source: Russian Science Foundation
Award Identifier / Grant number: 19-11-00019
Funding source: Bulgarian National Science Fund
Award Identifier / Grant number: KP-06-M32/2-17.12.2019
Funding statement: The study on the random walk algorithms and balanced Monte Carlo methods is supported by the RFBR and NSFB, project number 20-51-18009, and by the Russian Science Foundation under Grant 19-11-00019 in the part of global random walk on grid algorithms for general elliptic equations. Venelin Todorov is supported by the Bulgarian National Science Fund under Project KP-06-M32/2-17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics”.
References
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