Low-rank para-Hermitian matrix EVD via polynomial power method with deflation

Khattak, Faizan A. and Proudler, Ian K. and Weiss, Stephan (2023) Low-rank para-Hermitian matrix EVD via polynomial power method with deflation. In: 9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2023-12-10 - 2023-12-13.

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Abstract

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.

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