Searching beyond SVD for rank reduction

Singular value decomposition (SVD) is analytically inherent in various reduced rank filters and/or estimators. But the computation of SVD is generally not an efficient way for rank reduction. This paper introduces an efficient approach to computing for rank reduction. This approach, referred to as the alternate power (AP) method, is globally and exponentially convergent under a weak condition, and is a generalization of the conventional power method for subspace computation. The AP method is especially useful for computing the reduced rank filter (RRF) by Brillinger (1975), the reduced rank Wiener filter (RRWF) by Scharf (1991), and the reduced rank maximum likelihood estimate (RRMLE) by Stoica and Viberg (1996).