Coarse grained parallel monte Carlo algorithms for solving SLAE using PVM
The problem of solving System of Linear Algebraic Equations (SLAE) by parallel Monte Carlo numerical methods is considered. Three Monte Carlo algorithms are presented. In case when copy of the matrix is sent to each processor the execution time for solving SLAE by Monte Carlo on p processors is bounded by O(nNT/p) (excluding the initial loading of the data) where N is the number of chains and T is the length of the chain in the stochastic process, which are independent of matrix size n. Numerical tests are performed for a number of dense and sparse test matrices using PVM on a cluster of workstations.
Alexandrov, V., Dehne, F, Rau-Chaplin, A., & Taft, K. (1998). Coarse grained parallel monte Carlo algorithms for solving SLAE using PVM. doi:10.1007/BFb0056591