Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

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

Research output: Contribution to conferencePaper

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.

Conference

ConferenceIEEE Sensor Signal Processing in Defence Conference
Abbreviated titleSSPD'17
CountryUnited Kingdom
CityLondon
Period6/12/177/12/17
Internet address

Fingerprint

Polynomials
Decomposition

Keywords

  • polynomial matrices
  • polynomial matrix eigenvalue decomposition
  • parahermitian matrices

Cite this

Coutts, F. K., Corr, J., Thompson, K., Proudler, I. K., & Weiss, S. (Accepted/In press). Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices. Paper presented at IEEE Sensor Signal Processing in Defence Conference, London, United Kingdom.
Coutts, Fraser K. ; Corr, Jamie ; Thompson, Keith ; Proudler, Ian K. ; Weiss, Stephan. / Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices. Paper presented at IEEE Sensor Signal Processing in Defence Conference, London, United Kingdom.5 p.
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Coutts, FK, Corr, J, Thompson, K, Proudler, IK & Weiss, S 2017, 'Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices' Paper presented at IEEE Sensor Signal Processing in Defence Conference, London, United Kingdom, 6/12/17 - 7/12/17, .

Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices. / Coutts, Fraser K.; Corr, Jamie; Thompson, Keith; Proudler, Ian K.; Weiss, Stephan.

2017. Paper presented at IEEE Sensor Signal Processing in Defence Conference, London, United Kingdom.

Research output: Contribution to conferencePaper

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

PY - 2017/9/6

Y1 - 2017/9/6

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/

M3 - Paper

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Coutts FK, Corr J, Thompson K, Proudler IK, Weiss S. Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices. 2017. Paper presented at IEEE Sensor Signal Processing in Defence Conference, London, United Kingdom.