Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

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

doi:10.1109/SSPD.2017.8233228

Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

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

Electronic And Electrical Engineering

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

7 Citations (Scopus)

41 Downloads (Pure)

Abstract

A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays.

Original language	English
Number of pages	5
DOIs	https://doi.org/10.1109/SSPD.2017.8233228
Publication status	Published - 21 Dec 2017
Event	IEEE Sensor Signal Processing in Defence Conference - London, London, United Kingdom Duration: 6 Dec 2017 → 7 Dec 2017 http://www.sspdconference.org

Conference

Conference	IEEE Sensor Signal Processing in Defence Conference
Abbreviated title	SSPD'17
Country/Territory	United Kingdom
City	London
Period	6/12/17 → 7/12/17
Internet address	http://www.sspdconference.org

Keywords

polynomial matrices
polynomial matrix eigenvalue decomposition
parahermitian matrices

Access to Document

10.1109/SSPD.2017.8233228

Coutts-etal-IEEE-SSPD-2017-Dovode-and-conquer-sequential-matrix-diagonalisationAccepted author manuscript, 196 KB

Cite this

@conference{2a94ef62a3c04f78b845e5a4013fde5a,

title = "Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices",

abstract = "A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays.",

keywords = "polynomial matrices, polynomial matrix eigenvalue decomposition, parahermitian matrices",

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

note = "{\textcopyright} Copyright 2017 IEEE - All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. F. Coutts, J. Corr, K. Thompson, I. Proudler and S. Weiss, {"}Divide-and-Conquer Sequential Matrix Diagonalisation for Parahermitian Matrices,{"} 2017 Sensor Signal Processing for Defence Conference (SSPD), London, UK, 2017, pp. 1-5, doi: 10.1109/SSPD.2017.8233228.; IEEE Sensor Signal Processing in Defence Conference, SSPD'17 ; Conference date: 06-12-2017 Through 07-12-2017",

year = "2017",

month = dec,

day = "21",

doi = "10.1109/SSPD.2017.8233228",

language = "English",

url = "http://www.sspdconference.org",

}

TY - CONF

T1 - Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

AU - Coutts, Fraser K.

AU - Corr, Jamie

AU - Thompson, Keith

AU - Proudler, Ian K.

AU - Weiss, Stephan

N1 - © Copyright 2017 IEEE - All rights reserved, including rights for text and data mining and training of artificial intelligence and similar technologies. F. Coutts, J. Corr, K. Thompson, I. Proudler and S. Weiss, "Divide-and-Conquer Sequential Matrix Diagonalisation for Parahermitian Matrices," 2017 Sensor Signal Processing for Defence Conference (SSPD), London, UK, 2017, pp. 1-5, doi: 10.1109/SSPD.2017.8233228.

PY - 2017/12/21

Y1 - 2017/12/21

N2 - A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays.

AB - A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays.

KW - polynomial matrices

KW - polynomial matrix eigenvalue decomposition

KW - parahermitian matrices

UR - http://sspd.eng.ed.ac.uk/

U2 - 10.1109/SSPD.2017.8233228

DO - 10.1109/SSPD.2017.8233228

M3 - Paper

T2 - IEEE Sensor Signal Processing in Defence Conference

Y2 - 6 December 2017 through 7 December 2017

ER -

Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Signal Processing Solutions for the Networked Battlespace

Cite this

Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Signal Processing Solutions for the Networked Battlespace

Cite this