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Abstract. The problem of solving systems of linear algebraic equations by parallel Monte Carlo numerical methods is considered. A parallel Monte Carlo method with relaxation is presented. This is a report of a research in progress, showing the effectiveness of this algorithm. Theoretical justification of this algorithm and numerical experiments are presented. The algorithms were implemented on a cluster of workstations using MPI.

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The problem of solving systems of linear algebraic equations by parallel Monte Carlo numerical methods is considered. A parallel Monte Carlo method with relaxation parameter and dispersion reduction using antithetic variates is presented. This is a report of a research in progress, showing the effectiveness of this algorithm. Theoretical justification of this algorithm and numerical experiments are presented. The algorithms were implemented on a cluster of workstations using MPI. Keyword: Monte Carlo method, Linear solver, Systems of linear algebraic equations, Parallel algorithms. Now at SHARCNET,