A Novel Neural Network Model for Extracting the Largest Sum of Real Part and Imaginary Part of Eigenvalues and the Corresponding Eigenvectors of a Real Matrix

DOI

10.2991/ceis-16.2016.14How to use a DOI?

Keywords

complex neural network; real matrix; maximum sum of real part and imaginary part; eigenvalue; eigenvector

Abstract

In this study, we proposed a novel complex neural network model, which extends the neural networks based approaches that can asymptotically compute the largest imaginary part or the largest real part of eigenvalues to the case of directly calculating the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvectors of a real matrix. The proposed neural network algorithm is described by a group of complex differential equations. And the algorithm has parallel processing ability in an asynchronous manner and could achieve high computing capability. This paper also provides a rigorous mathematical proof for its convergence for a more clear understanding of network dynamic behaviors relating to the computation of the eigenvector and the eigenvalue. Numerical examples showed that the proposed algorithm has good performance for a general real matrix.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Hang Tan
AU  - Xue-Song Liang
AU  - Li-Ping Wan
AU  - Zhao-Yao Wu
PY  - 2016/11
DA  - 2016/11
TI  - A Novel Neural Network Model for Extracting the Largest Sum of Real Part and Imaginary Part of Eigenvalues and the Corresponding Eigenvectors of a Real Matrix
BT  - Proceedings of the 2016 International Conference on Computer Engineering and Information Systems
PB  - Atlantis Press
SP  - 68
EP  - 72
SN  - 2352-538X
UR  - https://doi.org/10.2991/ceis-16.2016.14
DO  - 10.2991/ceis-16.2016.14
ID  - Tan2016/11
ER  -