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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 84
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 95
A Scalable Parallel Genetic Algorithm for Solving Linear Systems G. Molnárka
Department of Mathematics and Computer Science, Széchenyi István University, Gyor, Hungary Full Bibliographic Reference for this paper
, "A Scalable Parallel Genetic Algorithm for Solving Linear Systems", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Fifth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 95, 2006. doi:10.4203/ccp.84.95
Keywords: linear system of equations, iterative algorithms, genetic algorithms, parallel algorithm.
Summary
For solving linear system of equations there are several algorithms. Iteration
algorithms are recommended for large linear systems with sparse matrix. But in
the case of general non-symmetrical or
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Let A be a general where ![]() ![]() where ![]()
Theorem: Let
and similar expressions for the vectors ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
Using the results of the theorem we can formulate a parallel algorithm, which
generates an approximate solution sequence xk,
The algorithm suggested based on the minimization of square of the residuum of the approximate solution in arbitrarily chosen dimension subspaces in parallel. Coupling of these parallel processes can be made, because the algorithm has got some genetic character. The fact, that the subspace dimension is freely chosen offers a scaling possibility for the algorithm and simple methods for different load balancing techniques. References
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