Parallel Monte Carlo algorithms for sparse SLAE using MPI

Abstract

The problem of solving sparse Systems of Linear Algebraic Equations (SLAE) by parallel Monte Carlo numerical methods is considered. The almost optimal Monte Carlo algorithms are presented. In case when a copy of the non-zero matrix elements is sent to each processor the execution time for solving SLAE by Monte Carlo on p processors is bounded by O(nNdT/p) where N is the number of chains, T is the length of the chain in the stochastic process, which are independent of matrix size n, and d is the average number of non-zero elements in the row. Finding a component of the solution vector requires O(NdT/p) time on p processors, which is independent of the matrix size n.