A Unified Self-Stabilizing Neural Network Algorithm for Principal Takagi Component Extraction

In this paper, we develop efficient methods for the computation of the Takagi components and the Takagi subspaces of complex symmetric matrices via the complex-valued neural network models. Firstly, we present a unified self-stabilizing neural network learning algorithm for principal Takagi components and study the stability of the proposed unified algorithms via the fixed-point analysis method. Secondly, the unified algorithm for extracting principal Takagi components is generalized to compute the principal Takagi subspace. Thirdly, we prove that the associated differential equations will globally asymptotically converge to an invariance set and the corresponding energy function attains a unique global minimum if and only if its state matrices span the principal Takagi subspace. Finally, numerical simulations are carried out to illustrate the theoretical results.