A simple functional neural network for computing the largest and smallest eigenvalues and corresponding eigenvectors of a real symmetric matrix

2005 ◽  
Vol 67 ◽  
pp. 369-383 ◽  
Author(s):  
Yiguang Liu ◽  
Zhisheng You ◽  
Liping Cao
Keyword(s):  
Neural Network ◽  
Symmetric Matrix ◽  
Real Symmetric Matrix ◽  
Functional Neural Network

Convergence Theory for Unified Discrete-Time RNNs with Quasi-Symmetric Connection

2014 ◽  
Vol 538 ◽  
pp. 167-170
Author(s):  
Hui Zhong Mao ◽  
Chen Qiao ◽  
Wen Feng Jing ◽  
Xi Chen ◽  
Jin Qin Mao
Keyword(s):  
Neural Network ◽  
Global Convergence ◽  
Discrete Time ◽  
Recurrent Neural Network ◽  
Symmetric Matrix ◽  
Network Models ◽  
Convergence Theory ◽  
Connection Matrix ◽  
Neural Network Models ◽  
Symmetric Connection

This paper presents the global convergence theory of the discrete-time uniform pseudo projection anti-monotone network with the quasi–symmetric matrix, which removes the connection matrix constraints. The theory widens the range of applications of the discrete–time uniform pseudo projection anti–monotone network and is valid for many kinds of discrete recurrent neural network models.

scholarly journals Cauchy's interlace theorem and lower bounds for the spectral radius

2000 ◽  
Vol 23 (8) ◽  
pp. 563-566 ◽  
Author(s):  
A. McD. Mercer ◽  
Peter R. Mercer
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Lower Bounds ◽  
Simple Proof ◽  
Symmetric Matrix ◽  
Real Symmetric Matrix

We present a short and simple proof of the well-known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.

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