Stable subspace tracking algorithm based on signed URV decomposition

The class of Schur subspace estimators provides a parametrization of all minimal-rank matrix approximants that lie within a specified distance of a given matrix, and in particular gives expressions for the column spans of these approximants. Unlike previous numerically unstable algorithms, this paper presents a signed URV decomposition (SURV) that efficiently and stably computes the Schur subspace estimator. Given a threshold on the singular values of the data matrix, SURV tracks the orthonormal basis of the principal/minor subspace and the rank of the subspace at the same time exactly with respect to the threshold at a computational complexity of O(m²) per vector update or downdate. SURV is not an iterative method.