Goulianas, K., Margaris, A. and Adamopoulos, M. (2013) Finding All Real Roots of 3 × 3 Nonlinear Algebraic Systems Using Neural Networks. Applied Mathematics and Computation, 219, 4444-4464.
http://dx.doi.org/10.1016/j.amc.2012.10.049

has been cited by the following article:

• TITLE: A Back Propagation-Type Neural Network Architecture for Solving the Complete n × n Nonlinear Algebraic System of Equations

  AUTHORS: Konstantinos Goulianas, Athanasios Margaris, Ioannis Refanidis, Konstantinos Diamantaras, Theofilos Papadimitriou

  KEYWORDS: Nonlinear Algebraic Systems, Neural Networks, Back Propagation, Numerical Analysis, Computational Methods

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.6, May 31, 2016

  ABSTRACT: The objective of this research is the presentation of a neural network capable of solving complete nonlinear algebraic systems of n equations with n unknowns. The proposed neural solver uses the classical back propagation algorithm with the identity function as the output function, and supports the feature of the adaptive learning rate for the neurons of the second hidden layer. The paper presents the fundamental theory associated with this approach as well as a set of experimental results that evaluate the performance and accuracy of the proposed method against other methods found in the literature.