Letters: Recurrent neural network model for computing largest and smallest generalized eigenvalue

Authors:
Lijun Liu;Hongmei Shao;Dong Nan
Affiliations:
School of Electronics and Information Engineering, Dalian University of Technology, Dalian 116624, China and Department of Mathematics, Dalian Nationalities University, Dalian 116605, China;Department of Mathematics, China University of Petroleum, Dongying 266555, China;Department of Mathematics and Physics, Beijing University of Technology, Beijing 100022, China
Venue:
Neurocomputing
Year:
2008

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Abstract

A continuous recurrent neural network model is presented for computing the largest and smallest generalized eigenvalue of a symmetric positive pair (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 as well as maintaining invariant norm property. Numerical simulation further shows the effectiveness of the proposed model.