Modeling and Analyzing Neural Networks Using Reproducing Kernel Hilbert Space Algorithm

Authors

Zainah Momani, Department of Computer Science, King Abdullah II School of Information Technology, The University of Jordan, Amman 11942, JordanFollow
Mohammad Al Shridah, Department of Computer Science, King Abdullah II School of Information Technology, The University of Jordan, Amman 11942, JordanFollow
Omar Abu Arqub, Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, JordanFollow
Mohammad Al-Momani, Department of Management Information Systems, Faculty of Economics and Administrative Sciences, Zarqa University, Zarqa 13132, JordanFollow
Shaher Momani, Department of Mathmatics,The University of Jordan, Amman 11942, Jordan. \\ Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Kingdom of Saudi ArabiaFollow

Author Country (or Countries)

Jordan

Abstract

In this paper, we present a new method for solving some certain differential systems in the artificial neural networks field. The analytic and approximate solutions are given with series form in the spaces W[a,b] and H[a,b]. The method used in this thesis has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical, physical, and engineering problems; second, it is accurate, need less effort to achieve the results, and is developed especially for the nonlinear cases; third, in the proposed method, it is possible to pick any point in the interval of integration and as well the approximate solutions will be applicable; fourth, the method does not require discretization of the variables, and it is not effected by computation round off errors and one is not faced with necessity of large computer memory and time. Results presented in this thesisshow potentiality, generality, and superiority of our method as compared with the Range Kutta method.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/120108

Recommended Citation

Momani, Zainah; Al Shridah, Mohammad; Abu Arqub, Omar; Al-Momani, Mohammad; and Momani, Shaher (2018) "Modeling and Analyzing Neural Networks Using Reproducing Kernel Hilbert Space Algorithm," Applied Mathematics & Information Sciences: Vol. 12: Iss. 1, Article 8.
DOI: http://dx.doi.org/10.18576/amis/120108
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss1/8