An Algorithm for Subspace Computation, with Applications in Signal Processing
Daniel R. Fuhrmann · SIAM Journal on Matrix Analysis and Applications · 1988
An algorithm for computing the eigenvectors corresponding to the m algebraically smallest or largest eigenvalues of an $n \times n$ symmetric matrix ${\bf A}$ 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 ${\bf A}$ can change while the algorithm is in progress.