Adaptive Generalized Eigen-pair Extraction by A Combination of Normalization and Quasi-Newton Algorithm

摘要

In this technical report, for a given explicit knowledge of a matrix pencil, we first propose a pair of novel algorithms, which are deterministic discrete time (DDT) systems of the proposed adaptive algorithms, for estimating the generalized eigen-pair (eigenvector and eigenvalue) corresponding to the largest/smallest generalized eigenvalue. Second, we present a pair of adaptive algorithms corresponding to the proposed DDT systems. We also establish rigorous analyses showing that the sequence generated by the DDT systems, using any stepsize in a certain range, converges to the orthogonal projection of the initial estimate onto the generalized eigensubspace corresponding to the largest/smallest generalized eigenvalue. Numerical examples show the sound applicability and efficacy of the proposed adaptive algorithms.