A Complex Neural Network Algorithm for Computing the Largest Real Part Eigenvalue and the corresponding Eigenvector of a Real Matrix

Hang Tan, Xuesong Liang, Liping Wan
2016 Proceedings of the 2016 4th International Conference on Sensors, Mechatronics and Automation (ICSMA 2016)   unpublished
In this study, we propose a novel complex neural network algorithm, which extends the neural network based approaches that can asymptotically compute the largest or smallest eigenvalues and the corresponding eigenvectors of real symmetric matrices, to the case of directly calculating the largest real part eigenvalue and the corresponding eigenvector of a real matrix. The proposed neural network algorithm is described by a group of complex differential equations, which is deduced from the
more » ... ced from the classical neural network model. The proposed algorithm is a class of continuous time recurrent neural network (RNN), it has parallel processing ability in an asynchronous manner and could achieve high computing capability. This paper provides a rigorous mathematical proof for its convergence in the case of real matrices for a more clear understanding of network dynamic behaviors relating to the computation of eigenvector and eigenvalue. The proposed approach has obvious virtues such as fast convergence speed and non-sensitivity to initial value. Numerical examples showed that the proposed algorithm has good performance. The Proposed Complex Neural Network Model The classical neural network algorithm for computing the eigenvector corresponding to the modulus maximum eigenvalue or modulus minimum eigenvalue can be illustrated as follows [5, 6]
doi:10.2991/icsma-16.2016.100 fatcat:2ss25nlnh5holhoqtya2yzmlsa