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International Journal of Industrial Mathematics
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Jafarian, A. (2015). On the convergence speed of artificial neural networks in‎ ‎the solving of linear ‎systems. International Journal of Industrial Mathematics, 7(1), 35-43.
A. Jafarian. "On the convergence speed of artificial neural networks in‎ ‎the solving of linear ‎systems". International Journal of Industrial Mathematics, 7, 1, 2015, 35-43.
Jafarian, A. (2015). 'On the convergence speed of artificial neural networks in‎ ‎the solving of linear ‎systems', International Journal of Industrial Mathematics, 7(1), pp. 35-43.
Jafarian, A. On the convergence speed of artificial neural networks in‎ ‎the solving of linear ‎systems. International Journal of Industrial Mathematics, 2015; 7(1): 35-43.

On the convergence speed of artificial neural networks in‎ ‎the solving of linear ‎systems

Article 4, Volume 7, Issue 1, Winter 2015, Page 35-43  XML PDF (852 K)
Document Type: Research Paper
Author
A. Jafarian
Department of Mathematics‎, ‎Urmia‎ ‎Branch‎, ‎Islamic Azad University‎, ‎Urmia‎, ‎Iran.‎
Abstract
‎Artificial neural networks have the advantages such as learning, ‎adaptation‎, ‎fault-tolerance‎, ‎parallelism and generalization‎. ‎This ‎paper is a scrutiny on the application of diverse learning methods‎ ‎in speed of convergence in neural networks‎. ‎For this aim‎, ‎first we ‎introduce a perceptron method based on artificial neural networks‎ ‎which has been applied for solving a non-singular system of linear ‎equations‎. ‎Next two famous learning techniques namely‎, ‎the‎ ‎steepest descent and quasi-Newton methods are employed to adjust ‎connection weights of the neural net‎. ‎The main aim of this study ‎is to compare ability and efficacy of the techniques in speed of‎ ‎convergence of the present neural net‎. ‎Finally‎, ‎we illustrate our ‎results on some numerical examples with computer ‎simulations.‎
Keywords
System of linear equations; Quasi-Newton method; Steepest descent‎ ‎method; Cost Function; Learning ‎algorithm
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