Compact order polynomial singular value decomposition of a matrix of analytic functions

Bakhit, Mohammed A. and Khattak, Faizan A. and Proudler, Ian K. and Weiss, Stephan and Rice, Garrey W. (2023) Compact order polynomial singular value decomposition of a matrix of analytic functions. In: 9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2023-12-10 - 2023-12-13. (https://doi.org/10.1109/CAMSAP58249.2023.10403445)

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Abstract

This paper presents a novel method for calculating a compact order singular value decomposition (SVD) of polynomial matrices, building upon the recently proven existence of an analytic SVD for analytic, non-multiplexed polynomial matrices. The proposed method calculates a conventional SVD in sample points on the unit circle, and then applies phase smoothing algorithms to establish phase-coherence between adjacent frequency bins. This results in the extraction of compact order singular values and their corresponding singular vectors. The method is evaluated through experiments conducted on an ensemble of randomised polynomial matrices, demonstrating its superior performance in terms of higher decomposition accuracy and lower polynomial order compared to state-of-the-art techniques.

ORCID iDs

Bakhit, Mohammed A., Khattak, Faizan A., Proudler, Ian K., Weiss, Stephan ORCID logoORCID: https://orcid.org/0000-0002-3486-7206 and Rice, Garrey W.;
CORE (COnnecting REpositories)