Efficient implementation of iterative polynomial matrix EVD algorithms exploiting structural redundancy and parallelisation

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Coutts, Fraser K. and Proudler, Ian K. and Weiss, Stephan (2019) Efficient implementation of iterative polynomial matrix EVD algorithms exploiting structural redundancy and parallelisation. IEEE Transactions on Circuits and Systems I: Regular Papers, 66 (12). pp. 4753-4766. ISSN 1549-8328 (https://doi.org/10.1109/TCSI.2019.2937006)

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Abstract

A number of algorithms are capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD), which is a generalisation of the EVD and will diagonalise a parahermitian polynomial matrix via paraunitary operations. While offering promising results in various broadband array processing applications, the PEVD has seen limited deployment in hardware due to the high computational complexity of these algorithms. Akin to low complexity divide-and-conquer (DaC) solutions to eigenproblems, this paper addresses a partially parallelisable DaC approach to the PEVD. A novel algorithm titled parallel-sequential matrix diagonalisation exhibits significantly reduced algorithmic complexity and run-time when compared with existing iterative PEVD methods. The DaC approach, which is shown to be suitable for multi-core implementation, can improve eigenvalue resolution at the expense of decomposition mean squared error, and offers a trade-off between the approximation order and accuracy of the resulting paraunitary matrices.

ORCID iDs

Coutts, Fraser K. ORCID logoORCID: https://orcid.org/0000-0003-2299-2648, Proudler, Ian K. and Weiss, Stephan ORCID logoORCID: https://orcid.org/0000-0002-3486-7206;
  • Item type:Article
    ID code:69429
    Dates:
    Date
    Event
    6 December 2019
    Published
    25 September 2019
    Published Online
    18 August 2019
    Accepted
    Notes:© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Subjects:Technology > Electrical engineering. Electronics Nuclear engineering
    Department:Faculty of Engineering > Electronic and Electrical Engineering
    Depositing user: Pure Administrator
    Date deposited:20 Aug 2019 13:39
    Last modified:22 Dec 2024 01:23
    URI:https://strathprints.strath.ac.uk/id/eprint/69429
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