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 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.