Implementation of Monte Carlo Algorithms for Eigenvalue Problem Using MPI
نویسندگان
چکیده
The problem of evaluating the dominant eigenvalue of real matrices using Monte Carlo numerical methods is considered. Three almost optimal Monte Carlo algorithms are presented: – Direct Monte Carlo algorithm (DMC) for calculating the largest eigenvalue of a matrix A. The algorithm uses iterations with the given matrix. – Resolvent Monte Carlo algorithm (RMC) for calculating the smallest or the largest eigenvalue. The algorithm uses Monte Carlo iterations with the resolvent matrix and includes parameter controlling the rate of convergence; – Inverse Monte Carlo algorithm (IMC) for calculating the smallest eigenvalue. The algorithm uses iterations with inverse matrix. Numerical tests are performed for a number of large sparse test matrices using MPI on a cluster of workstations.
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