A neurodynamic approach to compute the generalized eigenvalues of symmetric positive matrix pair

This paper shows that the generalized eigenvalues of a symmetric positive matrix pair can be computed efficiently under more general hypothesises by the proposed recurrent neural network (RNN) in Liu et al. (2008). More precisely, it is proved that based on more general hypothesises, the state solution of the proposed RNN converges to the generalized eigenvector of symmetric positive pair, and its related generalized eigenvalue depends on the initial point of the state solution. Furthermore, the related largest and smallest generalized eigenvalues can also be obtained by the proposed RNN. Some related numerical experiments are also presented to illustrate our results.