Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Scalable parallel geometric algorithms for coarse grained multicomputers
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Matrix computations (3rd ed.)
Comparison of Three Monte Carlo Methods for Matrix Inversion
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing-Volume II
Implementation of Monte Carlo Algorithms for Eigenvalue Problem Using MPI
Proceedings of the 5th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Sequential Monte Carlo Techniques for the Solution of Linear Systems
Sequential Monte Carlo Techniques for the Solution of Linear Systems
Mixed Monte Carlo Parallel Algorithms for Matrix Computation
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Hybrid Monte Carlo Methods for Matrix Computation
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
A sparse parallel hybrid monte carlo algorithm for matrix computations
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Parallel hybrid monte carlo algorithms for matrix computations
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
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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.