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

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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.
Original languageEnglish
Pages1-5
Number of pages5
Publication statusPublished - 13 Dec 2023
Event9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Los Suenos, Costa Rica
Duration: 10 Dec 202313 Dec 2023
https://camsap23.ig.umons.ac.be/

Workshop

Workshop9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Abbreviated titleCAMSAP
Country/TerritoryCosta Rica
CityLos Suenos
Period10/12/2313/12/23
Internet address

Keywords

  • power method
  • para-hermitian matrices
  • eigenvalue decomposition (EVD)

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  • Generalized polynomial power method

    Khattak, F. A., Proudler, I. K. & Weiss, S., 22 Sept 2023, 2023 Sensor Signal Processing for Defence Conference (SSPD). Piscataway, NJ: IEEE, 5 p.

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