Elsevier

Neurocomputing

Volume 7, Issue 2, March 1995, Pages 145-157
Neurocomputing

Paper
Real-time neural computation of the eigenvector corresponding to the largest eigenvalue of positive matrix

https://doi.org/10.1016/0925-2312(93)E0055-IGet rights and content

Abstract

This paper proposes a neural network approach to compute in real time the eigenvector corresponding to the largest eigenvalue of a positive matrix. We show analytically and by simulations that the proposed neural network is guaranteed to be stable and provides results arbitrarily close to the accurate eigenvector within an elapsed time of only a few characteristic time constants of the network. The parameters of the network such as interconnection strengths can be obtained from the given matrix without any computations. As a result, this proposed neural network is satisfactory for the real time application of signal processing in which it is desired to provide as fast as possible the eigenvector corresponding to the largest eigenvalue of a positive matrix.

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    Most of them are focused on computing the eigenvectors of symmetric matrices corresponding to the largest or the smallest eigenvalues. There are several results for the generalized eigenvalue problem with the symmetric-definite pairs [30–35]. [1,2]

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