A complex neural network algorithm for computing the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvector of a real normal matrix
- DOI
- 10.2991/eeeis-16.2017.88How to use a DOI?
- Keywords
- Complex neural network; Real normal matrix; Maximum sum of real part and imaginary part; Eigenvalue; Eigenvector.
- Abstract
In this study, we proposed a novel complex neural network algorithm, which extends the neural networks based approaches that can asymptotically compute the largest modulus of eigenvalues and the corresponding eigenvector to the case of directly computing the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvectors of a real normal 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 example showed that the proposed algorithm has good performance for a general real normal 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/).
Cite this article
TY - CONF AU - Hang Tan AU - Li-Ping Wan AU - Rong Ye AU - Xue-Song Liang AU - Zhao-Yao Wu PY - 2016/12 DA - 2016/12 TI - A complex neural network algorithm for computing the largest sum of real part and imaginary part of eigenvalues and the corresponding eigenvector of a real normal matrix BT - Proceedings of the 2nd Annual International Conference on Electronics, Electrical Engineering and Information Science (EEEIS 2016) PB - Atlantis Press SP - 716 EP - 723 SN - 2352-5401 UR - https://doi.org/10.2991/eeeis-16.2017.88 DO - 10.2991/eeeis-16.2017.88 ID - Tan2016/12 ER -