Low-Rank Para-Hermitian Matrix EVD via Polynomial Power Method with Deflation

The power method in conjunction with deflation provides an economical approach to compute an eigenvalue decomposition (EVD) of a low-rank Hermitian matrix, which typically appears as a covariance matrix in narrowband sensor array processing. In this paper, we extend this idea to the broadband case, where a polynomial para-Hermitian matrix needs to be diagonalised. For the low-rank case, we combine a polynomial equivalent of the power method with a deflation approach to subsequently extract eigenpairs. We present perturbation analysis and simulation results based on an ensemble of low-rank randomized para-Hermitian matrices. The proposed approach demonstrates higher accuracy, faster execution time, and lower implementation cost than state-of-the-art algorithms.