TRACKING A FEW EXTREME SINGULAR-VALUES AND VECTORS IN SIGNAL-PROCESSING

In various applications, it is necessary to keep track of a low-rank approximation of a covariance matrix, R(t), slowly varying with time. It is convenient to track the left singular vectors associated with the largest singular values of the triangular factor, L(t), of its Cholesky factorization. These algorithms are referred to as “square-root.” The drawback of the Eigenvalue Decomposition (EVD) or the Singular Value Decomposition (SVD) is usually the volume of the computations. Various numerical methods carrying out this task are surveyed in this paper, and we show why this admittedly heavy computational burden is questionable in numerous situations and should be revised. Indeed, the complexity per eigenpair is generally a quadratic function of the problem size, but there exist faster algorithms whose complexity is linear. Finally, in order to make a choice among the large and fuzzy set of available techniques, comparisons are made based on computer simulations in a relevant signal processing context. © 1990 IEEE