Abstract. 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 −1 C, 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.
This paper describes a prototype grid infrastructure, called the "eMinerals minigrid", for molecular simulation scientists. which is based on an integration of shared compute and data resources. We describe the key components, namely the use of Condor pools, Linux/Unix clusters with PBS and IBM's LoadLeveller job handling tools, the use of Globus for security handling, the use of Condor-G tools for wrapping globus job submit commands, Condor's DAGman tool for handling workflow, the Storage Resource Broker for handling data, and the CCLRC dataportal and associated tools for both archiving data with metadata and making data available to other workers.
Abstract. Computations involving Monte Carlo methods are, very often, easily and efficiently parallelized. P-GRADE is a parallel application development environment which provides an integrated set of programming tools for development of general message-passing applications to run in heterogeneous computing environments or supercomputers. In this paper, we show how Monte Carlo algorithms for solving Systems of Linear Equations and Matrix Inversion can easily be parallelized using P-GRADE.
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