An iterative DFT-based approach to the polynomial matrix eigenvalue decomposition

Fraser K. Coutts; Keith Thompson; Ian K. Proudler; Stephan Weiss

doi:10.1109/ACSSC.2018.8645226

An iterative DFT-based approach to the polynomial matrix eigenvalue decomposition

Fraser K. Coutts, Keith Thompson, Ian K. Proudler, Stephan Weiss

Electronic And Electrical Engineering

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

3 Citations (Scopus)

Abstract

As an extension of the ordinary EVD to polynomial matrices, the polynomial matrix eigenvalue decomposition (PEVD) will generate paraunitary matrices that diagonalise a parahermitian matrix. Frequency-based PEVD algorithms have shown promise for the decomposition of problems of finite order, but require a priori knowledge of the length of the decomposition. This paper presents a novel iterative frequency-based PEVD algorithm which can compute an accurate decomposition without requiring this information. We demonstrate through the use of simulations that the algorithm can achieve superior performance over existing iterative PEVD methods.

Original language	English
Title of host publication	2018 52nd Asilomar Conference on Signals, Systems, and Computers
Place of Publication	Piscataway, NJ
Publisher	IEEE
Number of pages	5
ISBN (Electronic)	9781538692189
ISBN (Print)	9781538692196
DOIs	https://doi.org/10.1109/ACSSC.2018.8645226
Publication status	Published - 21 Feb 2019
Event	52nd Asilomar Conference on Signals, Systems, and Computers - Pacific Grove, United States Duration: 28 Oct 2018 → 31 Oct 2018

Conference

Conference	52nd Asilomar Conference on Signals, Systems, and Computers
Country/Territory	United States
City	Pacific Grove
Period	28/10/18 → 31/10/18

Keywords

polynomial matrices
polynomial matrix eigenvalue decomposition (PEVD)
parahermitian matrix

Access to Document

10.1109/ACSSC.2018.8645226

Signal Processing Solutions for the Networked Battlespace
Soraghan, J. & Weiss, S.
EPSRC (Engineering and Physical Sciences Research Council)
1/04/13 → 31/03/18
Project: Research

Cite this

@inproceedings{a9301a829b78460a9978afbbf1f3f712,

title = "An iterative DFT-based approach to the polynomial matrix eigenvalue decomposition",

abstract = "As an extension of the ordinary EVD to polynomial matrices, the polynomial matrix eigenvalue decomposition (PEVD) will generate paraunitary matrices that diagonalise a parahermitian matrix. Frequency-based PEVD algorithms have shown promise for the decomposition of problems of finite order, but require a priori knowledge of the length of the decomposition. This paper presents a novel iterative frequency-based PEVD algorithm which can compute an accurate decomposition without requiring this information. We demonstrate through the use of simulations that the algorithm can achieve superior performance over existing iterative PEVD methods.",

keywords = "polynomial matrices, polynomial matrix eigenvalue decomposition (PEVD), parahermitian matrix",

author = "Coutts, {Fraser K.} and Keith Thompson and Proudler, {Ian K.} and Stephan Weiss",

year = "2019",

month = feb,

day = "21",

doi = "10.1109/ACSSC.2018.8645226",

language = "English",

isbn = "9781538692196",

booktitle = "2018 52nd Asilomar Conference on Signals, Systems, and Computers",

publisher = "IEEE",

note = "52nd Asilomar Conference on Signals, Systems, and Computers ; Conference date: 28-10-2018 Through 31-10-2018",

}

Coutts, FK, Thompson, K, Proudler, IK & Weiss, S 2019, An iterative DFT-based approach to the polynomial matrix eigenvalue decomposition. in 2018 52nd Asilomar Conference on Signals, Systems, and Computers. IEEE, Piscataway, NJ, 52nd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, United States, 28/10/18. https://doi.org/10.1109/ACSSC.2018.8645226

TY - GEN

T1 - An iterative DFT-based approach to the polynomial matrix eigenvalue decomposition

AU - Coutts, Fraser K.

AU - Thompson, Keith

AU - Proudler, Ian K.

AU - Weiss, Stephan

PY - 2019/2/21

Y1 - 2019/2/21

N2 - As an extension of the ordinary EVD to polynomial matrices, the polynomial matrix eigenvalue decomposition (PEVD) will generate paraunitary matrices that diagonalise a parahermitian matrix. Frequency-based PEVD algorithms have shown promise for the decomposition of problems of finite order, but require a priori knowledge of the length of the decomposition. This paper presents a novel iterative frequency-based PEVD algorithm which can compute an accurate decomposition without requiring this information. We demonstrate through the use of simulations that the algorithm can achieve superior performance over existing iterative PEVD methods.

AB - As an extension of the ordinary EVD to polynomial matrices, the polynomial matrix eigenvalue decomposition (PEVD) will generate paraunitary matrices that diagonalise a parahermitian matrix. Frequency-based PEVD algorithms have shown promise for the decomposition of problems of finite order, but require a priori knowledge of the length of the decomposition. This paper presents a novel iterative frequency-based PEVD algorithm which can compute an accurate decomposition without requiring this information. We demonstrate through the use of simulations that the algorithm can achieve superior performance over existing iterative PEVD methods.

KW - polynomial matrices

KW - polynomial matrix eigenvalue decomposition (PEVD)

KW - parahermitian matrix

U2 - 10.1109/ACSSC.2018.8645226

DO - 10.1109/ACSSC.2018.8645226

M3 - Conference contribution book

SN - 9781538692196

BT - 2018 52nd Asilomar Conference on Signals, Systems, and Computers

PB - IEEE

CY - Piscataway, NJ

T2 - 52nd Asilomar Conference on Signals, Systems, and Computers

Y2 - 28 October 2018 through 31 October 2018

ER -

An iterative DFT-based approach to the polynomial matrix eigenvalue decomposition

Abstract

Conference

Keywords

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Projects

Signal Processing Solutions for the Networked Battlespace

Cite this