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.
Over the period of 6 years and three phases, the SEE-GRID programme has
established a strong regional human network in the area of distributed
scientific computing and has set up a powerful regional Grid infrastructure. It
attracted a number of user communities and applications from diverse fields
from countries throughout the South-Eastern Europe. From the infrastructure
point view, the first project phase has established a pilot Grid infrastructure
with more than 20 resource centers in 11 countries. During the subsequent two
phases of the project, the infrastructure has grown to currently 55 resource
centers with more than 6600 CPUs and 750 TBs of disk storage, distributed in 16
participating countries. Inclusion of new resource centers to the existing
infrastructure, as well as a support to new user communities, has demanded
setup of regionally distributed core services, development of new monitoring
and operational tools, and close collaboration of all partner institution in
managing such a complex infrastructure. In this paper we give an overview of
the development and current status of SEE-GRID regional infrastructure and
describe its transition to the NGI-based Grid model in EGI, with the strong SEE
regional collaboration.Comment: 22 pages, 12 figures, 4 table
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