Extension of power method to para-Hermitian matrices: polynomial power method

Faizan Ahmad Khattak; Ian Proudler; Stephan Weiss

Extension of power method to para-Hermitian matrices: polynomial power method

Faizan Ahmad Khattak, Ian Proudler, Stephan Weiss

Electronic And Electrical Engineering

Research output: Contribution to conference › Paper › peer-review

207 Downloads (Pure)

Abstract

This document extends the idea of the power method to polynomial para-Hermitian matrices for the extraction of the principal analytic eigenpair. The proposed extension repeatedly multiplies a polynomial vector with a para-Hermitian matrix followed by an appropriate normalization in each iteration. To limit the order growth of the product vector, truncation is performed post-normalization in each iteration. The method is validated through simulation results over an ensemble of randomized para-Hermitian matrices and is shown to perform significantly better than state-of-the-art algorithms.

Original language	English
Pages	1-5
Number of pages	5
Publication status	E-pub ahead of print - 4 Sept 2023
Event	31st European Signal Processing Conference - Helsinki, Finland Duration: 4 Sept 2023 → 8 Sept 2023 https://eusipco2023.org/

Conference

Conference	31st European Signal Processing Conference
Abbreviated title	EUSIPCO'23
Country/Territory	Finland
City	Helsinki
Period	4/09/23 → 8/09/23
Internet address	https://eusipco2023.org/

Keywords

polynomial para-Hermitian matrices
eigenvalue decomposition (EVD)
narrowband power interations
polynomial power method

Access to Document

Khattak-etal-EUSIPCO-2023-Extension-of-power-method-to-para-Hermitian-matricesAccepted author manuscript, 598 KBLicence: CC BY 4.0

1 Finished

Signal Processing in the Information Age (UDRC III)
Weiss, S. (Principal Investigator) & Stankovic, V. (Co-investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 31/03/24
Project: Research

1 Conference contribution book

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.
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

Open Access
File
2 Citations (Scopus)

86 Downloads (Pure)

Cite this

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title = "Extension of power method to para-Hermitian matrices: polynomial power method",

abstract = "This document extends the idea of the power method to polynomial para-Hermitian matrices for the extraction of the principal analytic eigenpair. The proposed extension repeatedly multiplies a polynomial vector with a para-Hermitian matrix followed by an appropriate normalization in each iteration. To limit the order growth of the product vector, truncation is performed post-normalization in each iteration. The method is validated through simulation results over an ensemble of randomized para-Hermitian matrices and is shown to perform significantly better than state-of-the-art algorithms.",

keywords = "polynomial para-Hermitian matrices, eigenvalue decomposition (EVD), narrowband power interations, polynomial power method",

author = "Khattak, {Faizan Ahmad} and Ian Proudler and Stephan Weiss",

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language = "English",

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note = "31st European Signal Processing Conference, EUSIPCO'23 ; Conference date: 04-09-2023 Through 08-09-2023",

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T1 - Extension of power method to para-Hermitian matrices

T2 - 31st European Signal Processing Conference

AU - Khattak, Faizan Ahmad

AU - Proudler, Ian

AU - Weiss, Stephan

PY - 2023/9/4

Y1 - 2023/9/4

N2 - This document extends the idea of the power method to polynomial para-Hermitian matrices for the extraction of the principal analytic eigenpair. The proposed extension repeatedly multiplies a polynomial vector with a para-Hermitian matrix followed by an appropriate normalization in each iteration. To limit the order growth of the product vector, truncation is performed post-normalization in each iteration. The method is validated through simulation results over an ensemble of randomized para-Hermitian matrices and is shown to perform significantly better than state-of-the-art algorithms.

AB - This document extends the idea of the power method to polynomial para-Hermitian matrices for the extraction of the principal analytic eigenpair. The proposed extension repeatedly multiplies a polynomial vector with a para-Hermitian matrix followed by an appropriate normalization in each iteration. To limit the order growth of the product vector, truncation is performed post-normalization in each iteration. The method is validated through simulation results over an ensemble of randomized para-Hermitian matrices and is shown to perform significantly better than state-of-the-art algorithms.

KW - polynomial para-Hermitian matrices

KW - eigenvalue decomposition (EVD)

KW - narrowband power interations

KW - polynomial power method

M3 - Paper

SP - 1

EP - 5

Y2 - 4 September 2023 through 8 September 2023

ER -

Extension of power method to para-Hermitian matrices: polynomial power method

Abstract

Conference

Keywords

Access to Document

Fingerprint

Projects

Signal Processing in the Information Age (UDRC III)

Research output

Generalized polynomial power method

Cite this