Fast Adaptive Extraction Algorithm for Multiple Principal Generalized Eigenvectors

摘要

We consider adaptively extracting multiple principal generalized eigenvectors, which can be widely applied in modern signal processing. By using the deflation technique, the problem is reformulated into an unconstrained minimization problem. An adaptive sequential algorithm based on the Newton method is proposed to solve this problem. To improve its real-time performance, a parallel version of this algorithm is provided on the basis of certain approximation. Furthermore, a two-layer neural network is constructed to execute the adaptive algorithm. The asymptotic convergence of this algorithm is rigorously proved by stochastic approximation theory. The simulation results demonstrate the effectiveness of the proposed algorithms.