An Algorithm for Subspace Computation, with Applications in Signal Processing

An algorithm for computing the eigenvectors corresponding to the m algebraically smallest or largest eigenvalues of an n × n symmetric matrix A is described. The algorithm consists of repeated applications of the Rayleigh-Ritz procedure to a sequence of subspaces of dimension $m + 1$ which converges to the desired subspace. The method is closely related to the Lanczos method, but requires a constant amount of computation at each iteration. Applications of the algorithm include the adaptive covariance eigenstructure computation, in which the matrix A can change while the algorithm is in progress.