Notes on “Recurrent neural network model for computing largest and smallest generalized eigenvalue”

We show some mistakes in the paper “Recurrent neural network model for computing largest and smallest generalized eigenvalue, Neurocomputing 71 (2008) 3589–3594” using a counterexample. And another recurrent neural network (RNN) with invariant B  -norm is proposed for computing the largest or smallest generalized eigenvalue and the corresponding eigenvector of any symmetric positive pair (A,B)(A,B), which can be simply extended to compute the second largest or smallest generalized eigenvalue and the corresponding eigenvector based on the similar skills established in other literature. In addition, convergence of such RNN is proven rigorously. Simulation results demonstrate the computational capability of such model.