Numerically Stable Algorithms for Adaptive Generalized Minor Subspace Extraction

摘要

This paper presents numerically stable algorithms for adaptive generalized minor subspace extraction. We first propose two algorithms for extracting the generalized eigenvector corresponding to the smallest generalized eigenvalue (i) based on the power method and (ii) by extending the modified Oja-Xu MCA learning algorithm proposed by Peng and Yi ('07). Then, these algorithms are utilized to extract generalized minor subspace in combination with (i) an extension of dimensional reduction technique by Misono and Yamada ('08) and (ii) the Gram-Schmidt process. Numerical examples show that the proposed algorithms are faster and more numerically stable than the reduced-rank generalized eigenvector extraction (R-GEVE) algorithm ('08).