Adaptive algorithms for computing the principal Takagi vector of a complex symmetric matrix

In this paper, we present a unified framework for deriving and analyzing adaptive algorithms for computing the principal Takagi vector of a complex symmetric matrix. Eight systems of complex-valued ordinary differential equations (complex-valued ODEs) are derived and their convergence behavior is an...

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Bibliographic Details
Published in:Neurocomputing (Amsterdam) 2018-11, Vol.317, p.79-87
Main Authors: Che, Maolin, Qiao, Sanzheng, Wei, Yimin
Format: Article
Language:English
Subjects:
Adaptive algorithm
Asymptotic stability
Complex symmetric matrix
Principal Takagi vector
Takagi factorization
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Summary:In this paper, we present a unified framework for deriving and analyzing adaptive algorithms for computing the principal Takagi vector of a complex symmetric matrix. Eight systems of complex-valued ordinary differential equations (complex-valued ODEs) are derived and their convergence behavior is analyzed. We prove that the solutions of the complex-valued ODEs are asymptotically stable. The systems can be implemented on neural networks. Finally, we show experimental results to support our analyses.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2018.07.064