Ebrahim Ganjalipour - Department of Mathematics and Computer Sciences, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Khadijeh Nemati - Department of Mathematics and Computer Sciences, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Amir Hosein Refahi Sheikhani - Department of Mathematics and Computer Sciences, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Hashem Saberi Najafi - Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran.

In this paper we proposed a new neurodynamic model with recurrent learning process for solving ill-condition Generalized eigenvalue problem (GEP) Ax = lambda Bx. our method is based on recurrent neural networks with customized energy function for finding smallest (largest) or all eigenpairs. We evaluate our method on collected structural engineering data from Harwell Boeing collection with high dimensional parameter space and ill-conditioned sparse matrices. The experiments demonstrate that our algorithm using Adam optimizer, in comparison with other stochastic optimization methods like gradient descent works well in practice and improves complexity and accuracy of convergence.

Recurrent Neural Network, eigenpairs, Adam Optimizer, positive definite matrix, ill-condition