The fast householder Bi-SVD subspace tracking algorithm

A new bi-iteration type subspace tracker for updating a rank-r   SVD approximant of a time-varying cross-correlation matrix of dimension N×MN×M is introduced. The algorithm is based on updated orthonormal-square (QS  ) decompositions with row-Householder reflections and attains a dominant complexity of 3Nr+3Mr3Nr+3Mr operations per time update, which is the lower bound of dominant complexity for an algorithm of this kind. A closed-form quasicode listing of the algorithm is provided. Computer experiments validate the theoretical results.