Complexity and search space reduction in cyclic-by-row PEVD algorithms

Research output: Contribution to conferencePaper

Abstract

In recent years, several 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 uses paraunitary operations to diagonalise a parahermitian matrix. This paper addresses potential computational savings that can be applied to existing cyclic-by-row approaches for the PEVD. These savings are found during the search and rotation stages, and do not significantly impact on algorithm accuracy. We demonstrate that with the proposed techniques, computations can be significantly reduced. The benefits of this are important for a number of broadband multichannel problems.

Conference

Conference50th Asilomar Conference on Signals, Systems and Computers
Abbreviated titleAsilomar 2016
CountryUnited States
CityPacific Grove, CA
Period6/11/169/11/16
Internet address

Fingerprint

Polynomials
Decomposition

Keywords

  • polynomial matrix eigenvalue decomposition
  • PEVD
  • space-time covariance matrices
  • algorithmic cost reductions
  • SMDCbR
  • sequential matrix diagonalisation

Cite this

Coutts, F. K., Corr, J., Thompson, K., Weiss, S., Proudler, I. K., & McWhirter, J. G. (Accepted/In press). Complexity and search space reduction in cyclic-by-row PEVD algorithms. Paper presented at 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States.
Coutts, Fraser K. ; Corr, Jamie ; Thompson, Keith ; Weiss, Stephan ; Proudler, Ian K. ; McWhirter, John G. . / Complexity and search space reduction in cyclic-by-row PEVD algorithms. Paper presented at 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States.5 p.
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abstract = "In recent years, several 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 uses paraunitary operations to diagonalise a parahermitian matrix. This paper addresses potential computational savings that can be applied to existing cyclic-by-row approaches for the PEVD. These savings are found during the search and rotation stages, and do not significantly impact on algorithm accuracy. We demonstrate that with the proposed techniques, computations can be significantly reduced. The benefits of this are important for a number of broadband multichannel problems.",
keywords = "polynomial matrix eigenvalue decomposition, PEVD, space-time covariance matrices, algorithmic cost reductions, SMDCbR, sequential matrix diagonalisation",
author = "Coutts, {Fraser K.} and Jamie Corr and Keith Thompson and Stephan Weiss and Proudler, {Ian K.} and McWhirter, {John G.}",
year = "2016",
month = "7",
day = "19",
language = "English",
note = "50th Asilomar Conference on Signals, Systems and Computers, Asilomar 2016 ; Conference date: 06-11-2016 Through 09-11-2016",
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Coutts, FK, Corr, J, Thompson, K, Weiss, S, Proudler, IK & McWhirter, JG 2016, 'Complexity and search space reduction in cyclic-by-row PEVD algorithms' Paper presented at 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States, 6/11/16 - 9/11/16, .

Complexity and search space reduction in cyclic-by-row PEVD algorithms. / Coutts, Fraser K.; Corr, Jamie; Thompson, Keith; Weiss, Stephan; Proudler, Ian K.; McWhirter, John G. .

2016. Paper presented at 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Complexity and search space reduction in cyclic-by-row PEVD algorithms

AU - Coutts, Fraser K.

AU - Corr, Jamie

AU - Thompson, Keith

AU - Weiss, Stephan

AU - Proudler, Ian K.

AU - McWhirter, John G.

PY - 2016/7/19

Y1 - 2016/7/19

N2 - In recent years, several 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 uses paraunitary operations to diagonalise a parahermitian matrix. This paper addresses potential computational savings that can be applied to existing cyclic-by-row approaches for the PEVD. These savings are found during the search and rotation stages, and do not significantly impact on algorithm accuracy. We demonstrate that with the proposed techniques, computations can be significantly 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 eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and uses paraunitary operations to diagonalise a parahermitian matrix. This paper addresses potential computational savings that can be applied to existing cyclic-by-row approaches for the PEVD. These savings are found during the search and rotation stages, and do not significantly impact on algorithm accuracy. We demonstrate that with the proposed techniques, computations can be significantly reduced. The benefits of this are important for a number of broadband multichannel problems.

KW - polynomial matrix eigenvalue decomposition

KW - PEVD

KW - space-time covariance matrices

KW - algorithmic cost reductions

KW - SMDCbR

KW - sequential matrix diagonalisation

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

M3 - Paper

ER -

Coutts FK, Corr J, Thompson K, Weiss S, Proudler IK, McWhirter JG. Complexity and search space reduction in cyclic-by-row PEVD algorithms. 2016. Paper presented at 50th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States.