Generalised sequential matrix diagonalisation for the SVD of polynomial matrices
Khattak, Faizan A. and Proudler, Ian K. and McWhirter, John G. and Weiss, Stephan; (2023) Generalised sequential matrix diagonalisation for the SVD of polynomial matrices. In: 2023 Sensor Signal Processing for Defence Conference (SSPD). IEEE, GBR. ISBN 9798350337327 (https://doi.org/10.1109/SSPD57945.2023.10256848)
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Abstract
To extend the singular value decomposition (SVD) to matrices of polynomials, an existing algorithm — a polynomial version of the Kogbetliantz SVD — iteratively targets the largest off-diagonal elements, and eliminates these through delay and Givens operations. In this paper, we perform a complete diagonalisation of the matrix component that contains this maximum element, thereby transfering more off-diagonal energy per iteration step. This approach is motivated by — and represents a generalisation of — the sequential matrix diagonalisation method for parahermitian matrices. In simulations, we demonstrate the benefit of this generalised SMD over the Kogbetliantz approach, both in terms of diagonalisation and the order of the extracted factors.
ORCID iDs
Khattak, Faizan A., Proudler, Ian K., McWhirter, John G. and Weiss, Stephan ORCID: https://orcid.org/0000-0002-3486-7206;-
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Item type: Book Section ID code: 86045 Dates: DateEvent12 September 2023Published12 September 2023Published Online23 June 2023AcceptedSubjects: Technology > Electrical engineering. Electronics Nuclear engineering > Telecommunication Department: Faculty of Engineering > Electronic and Electrical Engineering
Technology and Innovation Centre > Sensors and Asset ManagementDepositing user: Pure Administrator Date deposited: 06 Jul 2023 00:39 Last modified: 03 Sep 2024 00:43 URI: https://strathprints.strath.ac.uk/id/eprint/86045