Monte Carlo methods for matrix computations on the grid

Authors:
S. Branford;C. Sahin;A. Thandavan;C. Weihrauch;V. N. Alexandrov;I. T. Dimov
Affiliations:
Centre for Advanced Computing and Emerging Technologies, School of System Engineering, Philip Lyle Building, The University of Reading, Whiteknights, PO Box 68, Reading, RG6 6BX, UK;Centre for Advanced Computing and Emerging Technologies, School of System Engineering, Philip Lyle Building, The University of Reading, Whiteknights, PO Box 68, Reading, RG6 6BX, UK;Centre for Advanced Computing and Emerging Technologies, School of System Engineering, Philip Lyle Building, The University of Reading, Whiteknights, PO Box 68, Reading, RG6 6BX, UK;Centre for Advanced Computing and Emerging Technologies, School of System Engineering, Philip Lyle Building, The University of Reading, Whiteknights, PO Box 68, Reading, RG6 6BX, UK;Centre for Advanced Computing and Emerging Technologies, School of System Engineering, Philip Lyle Building, The University of Reading, Whiteknights, PO Box 68, Reading, RG6 6BX, UK;Centre for Advanced Computing and Emerging Technologies, School of System Engineering, Philip Lyle Building, The University of Reading, Whiteknights, PO Box 68, Reading, RG6 6BX, UK and Institute ...
Venue:
Future Generation Computer Systems
Year:
2008

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Abstract

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors.