Multiple shift QR decomposition for polynomial matrices

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

Multiple shift QR decomposition for polynomial matrices

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

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Abstract

In recent years, several algorithms for the iterative calculation of a polynomial matrix QR decomposition (PQRD) have been introduced. The PQRD is a generalisation of the ordinary QRD and uses paraunitary operations to upper-triangularise a polynomial matrix. This paper addresses a multiple shift strategy that can be applied to an existing PQRD algorithm. We demonstrate that with the proposed strategy, the computation time of the algorithm can be reduced. The benefits of this are important for a number of broadband multichannel problems.

Original language	English
Title of host publication	11th IMA International Conference on Mathematics in Signal Processing
Pages	1-4
Number of pages	4
Publication status	Published - 12 Dec 2016
Event	11th IMA International Conference on Mathematics in Signal Processing - IET Austin Court, Birmingham, United Kingdom Duration: 12 Dec 2016 → 14 Dec 2016 http://www.ima.org.uk/conferences/conferences_calendar/11th_maths_in_signal_processing.html

Conference

Conference	11th IMA International Conference on Mathematics in Signal Processing
Country/Territory	United Kingdom
City	Birmingham
Period	12/12/16 → 14/12/16
Internet address	http://www.ima.org.uk/conferences/conferences_calendar/11th_maths_in_signal_processing.html

Keywords

polynomial matrix representations
QR decomposition
finite impulse response
sequential matrix diagonalisation
polynomial eigenvalue decomposition
PQRD by steps algorithms
polynomial matrices

Access to Document

Coutts-etal-IMAICMSP-2016-Multiple-shift-QR-decomposition-for-polynomial matricesAccepted author manuscript, 75.2 KB

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{dbf9c5f506ea473681a79fa033175a2c,

title = "Multiple shift QR decomposition for polynomial matrices",

abstract = "In recent years, several algorithms for the iterative calculation of a polynomial matrix QR decomposition (PQRD) have been introduced. The PQRD is a generalisation of the ordinary QRD and uses paraunitary operations to upper-triangularise a polynomial matrix. This paper addresses a multiple shift strategy that can be applied to an existing PQRD algorithm. We demonstrate that with the proposed strategy, the computation time of the algorithm can be reduced. The benefits of this are important for a number of broadband multichannel problems.",

keywords = "polynomial matrix representations, QR decomposition, finite impulse response, sequential matrix diagonalisation, polynomial eigenvalue decomposition, PQRD by steps algorithms, polynomial matrices",

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

year = "2016",

month = dec,

day = "12",

language = "English",

pages = "1--4",

booktitle = "11th IMA International Conference on Mathematics in Signal Processing",

note = "11th IMA International Conference on Mathematics in Signal Processing ; Conference date: 12-12-2016 Through 14-12-2016",

url = "http://www.ima.org.uk/conferences/conferences_calendar/11th_maths_in_signal_processing.html",

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TY - GEN

T1 - Multiple shift QR decomposition for polynomial matrices

AU - Coutts, Fraser K.

AU - Corr, Jamie

AU - Thompson, Keith

AU - Weiss, Stephan

AU - Proudler, Ian K.

AU - McWhirter, John G.

PY - 2016/12/12

Y1 - 2016/12/12

N2 - In recent years, several algorithms for the iterative calculation of a polynomial matrix QR decomposition (PQRD) have been introduced. The PQRD is a generalisation of the ordinary QRD and uses paraunitary operations to upper-triangularise a polynomial matrix. This paper addresses a multiple shift strategy that can be applied to an existing PQRD algorithm. We demonstrate that with the proposed strategy, the computation time of the algorithm can be reduced. The benefits of this are important for a number of broadband multichannel problems.

AB - In recent years, several algorithms for the iterative calculation of a polynomial matrix QR decomposition (PQRD) have been introduced. The PQRD is a generalisation of the ordinary QRD and uses paraunitary operations to upper-triangularise a polynomial matrix. This paper addresses a multiple shift strategy that can be applied to an existing PQRD algorithm. We demonstrate that with the proposed strategy, the computation time of the algorithm can be reduced. The benefits of this are important for a number of broadband multichannel problems.

KW - polynomial matrix representations

KW - QR decomposition

KW - finite impulse response

KW - sequential matrix diagonalisation

KW - polynomial eigenvalue decomposition

KW - PQRD by steps algorithms

KW - polynomial matrices

M3 - Conference contribution book

SP - 1

EP - 4

BT - 11th IMA International Conference on Mathematics in Signal Processing

T2 - 11th IMA International Conference on Mathematics in Signal Processing

Y2 - 12 December 2016 through 14 December 2016

ER -

Multiple shift QR decomposition for polynomial matrices

Abstract

Conference

Keywords

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Projects

Signal Processing Solutions for the Networked Battlespace

Cite this