Comparison of three Monte Carlo methods for Matrix Inversion
Three Monte Carlo methods for Matrix Inversion (MI) are considered: with absorption, without absorption with uniform transition frequency function, and without absorption with almost optimal transition frequency function.
Recently Alexandrov, Megson and Dimov has shown that an n×n matrix can be inverted in 3n/2 + N + T steps on regular arrays with O(n2NT) cells. A number of bounds on N and T have been established (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), which show that these designs are faster than the existing designs for large values of n.
In this paper we take another implementation approach, we consider parallel Monte Carlo algorithms for MI on MIMD environment, i.e. running on a cluster of workstations under PVM. The Monte Carlo method with almost optimal frequency function performs best of the three methods as it needs about six-ten times less chains for the same precision.
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