Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices

Jamie Corr, Keith Thompson, Stephan Weiss, John G. McWhirter, Soydan Redif, Ian K. Proudler

Research output: Contribution to conferencePaper

32 Citations (Scopus)

Abstract

A polynomial eigenvalue decomposition of paraher-mitian matrices can be calculated approximately using iterative approaches such as the sequential matrix diagonalisation (SMD) algorithm. In this paper, we present an improved SMD algorithm which, compared to existing SMD approaches, eliminates more off-diagonal energy per step. This leads to faster convergence while incurring only a marginal increase in complexity. We motivate the approach, prove its convergence, and demonstrate some results that underline the algorithm's performance.

Conference

Conference2014 IEEE Workshop on Statistical Signal Processing (SSP)
CountryUnited Kingdom
CityGold Coast
Period29/06/142/07/14

Fingerprint

Polynomials
Decomposition

Keywords

  • parahermitian polynomial matrices
  • SMD algorithm
  • polynomial eigenvalue decomposition

Cite this

Corr, J., Thompson, K., Weiss, S., McWhirter, J. G., Redif, S., & Proudler, I. K. (2014). Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices. 312-315. Paper presented at 2014 IEEE Workshop on Statistical Signal Processing (SSP) , Gold Coast, United Kingdom. https://doi.org/10.1109/SSP.2014.6884638
Corr, Jamie ; Thompson, Keith ; Weiss, Stephan ; McWhirter, John G. ; Redif, Soydan ; Proudler, Ian K. / Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices. Paper presented at 2014 IEEE Workshop on Statistical Signal Processing (SSP) , Gold Coast, United Kingdom.4 p.
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title = "Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices",
abstract = "A polynomial eigenvalue decomposition of paraher-mitian matrices can be calculated approximately using iterative approaches such as the sequential matrix diagonalisation (SMD) algorithm. In this paper, we present an improved SMD algorithm which, compared to existing SMD approaches, eliminates more off-diagonal energy per step. This leads to faster convergence while incurring only a marginal increase in complexity. We motivate the approach, prove its convergence, and demonstrate some results that underline the algorithm's performance.",
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author = "Jamie Corr and Keith Thompson and Stephan Weiss and McWhirter, {John G.} and Soydan Redif and Proudler, {Ian K.}",
note = "{\circledC} 2014 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.; 2014 IEEE Workshop on Statistical Signal Processing (SSP) ; Conference date: 29-06-2014 Through 02-07-2014",
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Corr, J, Thompson, K, Weiss, S, McWhirter, JG, Redif, S & Proudler, IK 2014, 'Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices' Paper presented at 2014 IEEE Workshop on Statistical Signal Processing (SSP) , Gold Coast, United Kingdom, 29/06/14 - 2/07/14, pp. 312-315. https://doi.org/10.1109/SSP.2014.6884638

Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices. / Corr, Jamie; Thompson, Keith; Weiss, Stephan; McWhirter, John G.; Redif, Soydan ; Proudler, Ian K.

2014. 312-315 Paper presented at 2014 IEEE Workshop on Statistical Signal Processing (SSP) , Gold Coast, United Kingdom.

Research output: Contribution to conferencePaper

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T1 - Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices

AU - Corr, Jamie

AU - Thompson, Keith

AU - Weiss, Stephan

AU - McWhirter, John G.

AU - Redif, Soydan

AU - Proudler, Ian K.

N1 - © 2014 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 - 2014/7

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N2 - A polynomial eigenvalue decomposition of paraher-mitian matrices can be calculated approximately using iterative approaches such as the sequential matrix diagonalisation (SMD) algorithm. In this paper, we present an improved SMD algorithm which, compared to existing SMD approaches, eliminates more off-diagonal energy per step. This leads to faster convergence while incurring only a marginal increase in complexity. We motivate the approach, prove its convergence, and demonstrate some results that underline the algorithm's performance.

AB - A polynomial eigenvalue decomposition of paraher-mitian matrices can be calculated approximately using iterative approaches such as the sequential matrix diagonalisation (SMD) algorithm. In this paper, we present an improved SMD algorithm which, compared to existing SMD approaches, eliminates more off-diagonal energy per step. This leads to faster convergence while incurring only a marginal increase in complexity. We motivate the approach, prove its convergence, and demonstrate some results that underline the algorithm's performance.

KW - parahermitian polynomial matrices

KW - SMD algorithm

KW - polynomial eigenvalue decomposition

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Corr J, Thompson K, Weiss S, McWhirter JG, Redif S, Proudler IK. Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices. 2014. Paper presented at 2014 IEEE Workshop on Statistical Signal Processing (SSP) , Gold Coast, United Kingdom. https://doi.org/10.1109/SSP.2014.6884638