Square-root QR inverse iteration for tracking the minor subspace

A new algorithm for tracking the eigenvectors associated with the r smallest eigenvalues of an N/spl times/N covariance matrix is introduced. The method is sequential inverse iteration based on a recursive square-root QR factor updating of the covariance matrix with O(N/sup 2/r) operations per time update. The principal operations count of this new tracker is justified by a significantly better performance compared with the fast O(Nr/sup 2/) minor subspace tracker of Douglas et al. (1998).