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

‎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