SVD-updating via constrained perturbations with application to subspace tracking

We propose new algorithms for approximate updating of the singular value decomposition (SVD) of an exponentially weighted data matrix after appending a new row. The algorithms are obtained in two steps: noise subspace sphericalization is first used to deflate the problem; the right singular vectors and the singular values are then efficiently updated by means of a constrained perturbation approach. The latter is based on Givens rotations and thus preserves the orthonormality of the updated singular vectors. The new algorithms have a complexity ranging from O(Nr) to O(Nr/sup 2/), where N and r respectively denote the data vector and signal-subspace dimensions. Their convergence behavior in subspace tracking applications is investigated by means of the ordinary differential equation (ODE) method and the results are supported by computer experiments.