A Convergence Analysis of G-NPAST Algorithm for Extracting the First Principal Generalized Eigenvector

摘要

In our previous work, we established the convergence analysis of the normalized projection approximation subspace tracking (NPAST) algorithm, for extracting the first principal eigenvector of an autocorrelation matrix, via a deterministic discrete time (DDT) approach. In this technical report, we extend the analysis to the convergence analysis of an algorithm (we call G-NPAST) by J. Yang et al. ('06), which is developed for generalized symmetric eigenvalue problem. Indeed, we have shown that G-NPAST is nothing but a generalization of NPAST. The proposed analysis shows that G-NPAST can be applied to the general case where the generalized eigenvalues are not necessarily distinct. Numerical examples further confirm the results.