Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms

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

doi:10.1109/EUSIPCO.2016.7760525

Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms

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

Electronic And Electrical Engineering

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

5 Citations (Scopus)

50 Downloads (Pure)

Abstract

A number of algorithms for the iterative calculation of 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. This paper addresses savings — both computationally and in terms of memory use — that exploit the parahermitian structure of the matrix being decomposed, and also suggests an implicit trimming approach to efficiently curb the polynomial order growth usually observed during iterations of the PEVD algorithms. We demonstrate that with the proposed techniques, both storage and computations can be significantly reduced, impacting on a number of broadband multichannel problems.

Original language	English
Title of host publication	2016 24th European Signal Processing Conference
Place of Publication	Piscataway
Publisher	IEEE
Pages	1633-1637
Number of pages	5
ISBN (Print)	9780992862657
DOIs	https://doi.org/10.1109/EUSIPCO.2016.7760525
Publication status	Published - 1 Dec 2016
Event	24th European Signal Processing Conference - Hilton Budapest, Budapest, Hungary Duration: 29 Aug 2016 → 2 Sep 2016 http://www.eusipco2016.org/

Publication series

Name
ISSN (Electronic)	2076-1465

Conference

Conference	24th European Signal Processing Conference
Abbreviated title	EUSIPCO'16
Country/Territory	Hungary
City	Budapest
Period	29/08/16 → 2/09/16
Internet address	http://www.eusipco2016.org/

Keywords

iterative calculation
polynomial matrices
polynomial matrix eigenvalue decomposition
parahermitian matrix
broadband multichannel problems
narrowband
diagonalization
diagonalisation

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10.1109/EUSIPCO.2016.7760525

Coutts-etal-EUSIPCO2016-Memory-and-complexity-reduction-in-parahermitian-matrix-manipulationsAccepted author manuscript, 149 KB

Cite this

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title = "Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms",

abstract = "A number of algorithms for the iterative calculation of 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. This paper addresses savings — both computationally and in terms of memory use — that exploit the parahermitian structure of the matrix being decomposed, and also suggests an implicit trimming approach to efficiently curb the polynomial order growth usually observed during iterations of the PEVD algorithms. We demonstrate that with the proposed techniques, both storage and computations can be significantly reduced, impacting on a number of broadband multichannel problems.",

keywords = "iterative calculation, polynomial matrices, polynomial matrix eigenvalue decomposition, parahermitian matrix, broadband multichannel problems, narrowband, diagonalization, diagonalisation",

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

note = "{\textcopyright} 2016 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.; 24th European Signal Processing Conference, EUSIPCO'16 ; Conference date: 29-08-2016 Through 02-09-2016",

year = "2016",

month = dec,

day = "1",

doi = "10.1109/EUSIPCO.2016.7760525",

language = "English",

isbn = "9780992862657",

publisher = "IEEE",

pages = "1633--1637",

booktitle = "2016 24th European Signal Processing Conference",

url = "http://www.eusipco2016.org/",

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Coutts, FK, Corr, J, Thompson, K, Weiss, S , Proudler, IK & McWhirter, JG 2016, Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms. in 2016 24th European Signal Processing Conference. IEEE, Piscataway, pp. 1633-1637, 24th European Signal Processing Conference, Budapest, Hungary, 29/08/16. https://doi.org/10.1109/EUSIPCO.2016.7760525

Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms. / Coutts, Fraser K.; Corr, Jamie; Thompson, Keith; Weiss, Stephan ; Proudler, Ian K.; McWhirter, John G. .

2016 24th European Signal Processing Conference. Piscataway : IEEE, 2016. p. 1633-1637.

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

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AU - Coutts, Fraser K.

AU - Corr, Jamie

AU - Thompson, Keith

AU - Weiss, Stephan

AU - Proudler, Ian K.

AU - McWhirter, John G.

N1 - © 2016 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.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - A number of algorithms for the iterative calculation of 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. This paper addresses savings — both computationally and in terms of memory use — that exploit the parahermitian structure of the matrix being decomposed, and also suggests an implicit trimming approach to efficiently curb the polynomial order growth usually observed during iterations of the PEVD algorithms. We demonstrate that with the proposed techniques, both storage and computations can be significantly reduced, impacting on a number of broadband multichannel problems.

AB - A number of algorithms for the iterative calculation of 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. This paper addresses savings — both computationally and in terms of memory use — that exploit the parahermitian structure of the matrix being decomposed, and also suggests an implicit trimming approach to efficiently curb the polynomial order growth usually observed during iterations of the PEVD algorithms. We demonstrate that with the proposed techniques, both storage and computations can be significantly reduced, impacting on a number of broadband multichannel problems.

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KW - polynomial matrices

KW - polynomial matrix eigenvalue decomposition

KW - parahermitian matrix

KW - broadband multichannel problems

KW - narrowband

KW - diagonalization

KW - diagonalisation

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UR - http://www.eusipco2016.org/

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DO - 10.1109/EUSIPCO.2016.7760525

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BT - 2016 24th European Signal Processing Conference

PB - IEEE

CY - Piscataway

T2 - 24th European Signal Processing Conference

Y2 - 29 August 2016 through 2 September 2016

ER -

Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms

Abstract

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Keywords

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Signal Processing Solutions for the Networked Battlespace

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Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms

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Publication series

Conference

Keywords

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Signal Processing Solutions for the Networked Battlespace

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