Fast orthogonal iteration adaptive algorithms for the generalized symmetric eigenproblem

A class of sequential orthogonal iteration updating algorithms for the time-varying generalized symmetric eigenproblem (GSE) is presented. These algorithms are maximally fast, requiring N/sup 2/+O(Nr) arithmetic operations each time step for tracking the r dominant eigenvectors and eigenvalues of an exponentially updated GSE of dimension N. Applications to subspace adaptive filtering and frequency estimation are also discussed. Detailed computer experiments lend empirical support to the theoretical findings.