Parallel Hybrid Monte Carlo Algorithms for Matrix Computations

Alexandrov, V. N., Atanassov, E., Dimov, I., Branford, S., Thandavan, A. and Wiehrauch, C. (2005) Parallel Hybrid Monte Carlo Algorithms for Matrix Computations. Lecture Notes In Computer Science, 3516. 752 - 759. doi: 10.1007/11428862_102

Abstract/Summary

In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D – C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D –1C, of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Further we run the algorithms on a mini-Grid and investigate their efficiency depending on the granularity. Corresponding experimental results are presented.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/15101
Item Type	Article
Refereed	Yes
Divisions	Science
Uncontrolled Keywords	Monte Carlo Method, Markov Chain, Matrix Inversion, Solution of System of Linear Equations, Grid Computing.
Download/View statistics	View download statistics for this item