Recurrent neural network model for computing largest and smallest generalized eigenvalue

A continuous recurrent neural network model is presented for computing the largest and smallest generalized eigenvalue of a symmetric positive pair (A,B)(A,B). Convergence properties to the extremum eigenvalues based upon Liapunov functional with the help of the generalized eigen-decomposition theorem is obtained. Compared with other existing models, this model is also suitable for computing the smallest generalized eigenvalue simply by replacing A   by -A-A as well as maintaining invariant norm property. Numerical simulation further shows the effectiveness of the proposed model.