Simple, effective computation of principal eigenvectors and their eigenvalues and application to high-resolution estimation of frequencies

We present the results of an investigation of the Prony-Lanczos (P-L) method [14], [38] and the power method [39] for simple computation of approximations to a few eigenvectors and eigenvalues of a Hermitian matrix. We are motivated by realization of high-resolution signal processing in an integrated circuit. The computational speeds of the above methods are analyzed. They are completely dependent on the speed of a matrix-vector product operation. If only a few eigenvalues or eigenvectors are needed, the suggested methods can substitute for methods of the LINPACK or EISPACK subroutine libraries. The accuracies of the suggested methods are evaluated using matrices formed from simulated data consisting of two sinusoids plus Gaussian noise. Comparisons are made to the corresponding eigenvalues and eigenvectors obtained using LINPACK as a reference. Also, the accuracies of frequency estimates obtained from the eigenvectors are compared.