Maximum energy sequential matrix diagonalisation for parahermitian matrices

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

doi:10.1109/ACSSC.2014.7094487

Maximum energy sequential matrix diagonalisation for parahermitian matrices

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

Electronic And Electrical Engineering

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

4 Citations (Scopus)

85 Downloads (Pure)

Abstract

Sequential matrix diagonalisation (SMD) refers to a family of algorithms to iteratively approximate a polynomial matrix eigenvalue decomposition. Key is to transfer as much energy as possible from off-diagonal elements to the diagonal per iteration, which has led to fast converging SMD versions involving judicious shifts within the polynomial matrix. Through an exhaustive search, this paper determines the optimum shift in terms of energy transfer. Though costly to implement, this scheme yields an important benchmark to which limited search strategies can be compared. In simulations, multiple-shift SMD algorithms can perform within 10% of the optimum energy transfer per iteration step.

Original language	English
Title of host publication	Conference Record of the Forty-Eighth Asilomar Conference on Signals, Systems & Computers
Editors	Michael B. Matthews
Place of Publication	Piscataway, NJ.
Publisher	IEEE
Pages	470-474
Number of pages	5
ISBN (Print)	9781479982950
DOIs	https://doi.org/10.1109/ACSSC.2014.7094487
Publication status	Published - 2014
Event	2014 48th Asilomar Conference on Signals, Systems and Computers - Pacific Grove, CA, United States Duration: 2 Nov 2014 → 5 Nov 2014

Conference

Conference	2014 48th Asilomar Conference on Signals, Systems and Computers
Country/Territory	United States
City	Pacific Grove, CA
Period	2/11/14 → 5/11/14

Keywords

channel coding
direction-of-arrival estimation
eigenvalues and eigenfunctions
iterative methods
polynomial matrices
precoding

Access to Document

10.1109/ACSSC.2014.7094487

Corr-etal-ACSSC-2015-Maximum-energy-sequntial-matrix-diagonalisation-for-parahermitian-matricesAccepted author manuscript, 177 KB

Cite this

@inproceedings{a8c983730df04c2b8561e50e33ce8249,

title = "Maximum energy sequential matrix diagonalisation for parahermitian matrices",

abstract = "Sequential matrix diagonalisation (SMD) refers to a family of algorithms to iteratively approximate a polynomial matrix eigenvalue decomposition. Key is to transfer as much energy as possible from off-diagonal elements to the diagonal per iteration, which has led to fast converging SMD versions involving judicious shifts within the polynomial matrix. Through an exhaustive search, this paper determines the optimum shift in terms of energy transfer. Though costly to implement, this scheme yields an important benchmark to which limited search strategies can be compared. In simulations, multiple-shift SMD algorithms can perform within 10% of the optimum energy transfer per iteration step.",

keywords = "channel coding, direction-of-arrival estimation, eigenvalues and eigenfunctions, iterative methods, polynomial matrices, precoding",

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

note = "(c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, 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 components of this work in other works.; 2014 48th Asilomar Conference on Signals, Systems and Computers ; Conference date: 02-11-2014 Through 05-11-2014",

year = "2014",

doi = "10.1109/ACSSC.2014.7094487",

language = "English",

isbn = "9781479982950",

pages = "470--474",

editor = "Matthews, {Michael B.}",

booktitle = "Conference Record of the Forty-Eighth Asilomar Conference on Signals, Systems & Computers",

publisher = "IEEE",

}

Corr, J, Thompson, K, Weiss, S, McWhirter, JG & Proudler, IK 2014, Maximum energy sequential matrix diagonalisation for parahermitian matrices. in MB Matthews (ed.), Conference Record of the Forty-Eighth Asilomar Conference on Signals, Systems & Computers. IEEE, Piscataway, NJ., pp. 470-474, 2014 48th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States, 2/11/14. https://doi.org/10.1109/ACSSC.2014.7094487

Maximum energy sequential matrix diagonalisation for parahermitian matrices. / Corr, Jamie; Thompson, Keith; Weiss, Stephan et al.
Conference Record of the Forty-Eighth Asilomar Conference on Signals, Systems & Computers. ed. / Michael B. Matthews. Piscataway, NJ.: IEEE, 2014. p. 470-474.

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

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AU - Corr, Jamie

AU - Thompson, Keith

AU - Weiss, Stephan

AU - McWhirter, John G.

AU - Proudler, Ian K.

N1 - (c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, 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 components of this work in other works.

PY - 2014

Y1 - 2014

N2 - Sequential matrix diagonalisation (SMD) refers to a family of algorithms to iteratively approximate a polynomial matrix eigenvalue decomposition. Key is to transfer as much energy as possible from off-diagonal elements to the diagonal per iteration, which has led to fast converging SMD versions involving judicious shifts within the polynomial matrix. Through an exhaustive search, this paper determines the optimum shift in terms of energy transfer. Though costly to implement, this scheme yields an important benchmark to which limited search strategies can be compared. In simulations, multiple-shift SMD algorithms can perform within 10% of the optimum energy transfer per iteration step.

AB - Sequential matrix diagonalisation (SMD) refers to a family of algorithms to iteratively approximate a polynomial matrix eigenvalue decomposition. Key is to transfer as much energy as possible from off-diagonal elements to the diagonal per iteration, which has led to fast converging SMD versions involving judicious shifts within the polynomial matrix. Through an exhaustive search, this paper determines the optimum shift in terms of energy transfer. Though costly to implement, this scheme yields an important benchmark to which limited search strategies can be compared. In simulations, multiple-shift SMD algorithms can perform within 10% of the optimum energy transfer per iteration step.

KW - channel coding

KW - direction-of-arrival estimation

KW - eigenvalues and eigenfunctions

KW - iterative methods

KW - polynomial matrices

KW - precoding

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DO - 10.1109/ACSSC.2014.7094487

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SN - 9781479982950

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BT - Conference Record of the Forty-Eighth Asilomar Conference on Signals, Systems & Computers

A2 - Matthews, Michael B.

PB - IEEE

CY - Piscataway, NJ.

T2 - 2014 48th Asilomar Conference on Signals, Systems and Computers

Y2 - 2 November 2014 through 5 November 2014

ER -

Maximum energy sequential matrix diagonalisation for parahermitian matrices

Abstract

Conference

Keywords

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Signal Processing Solutions for the Networked Battlespace

2014 48th Asilomar Conference on Signals, Systems and Computers

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Maximum energy sequential matrix diagonalisation for parahermitian matrices

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

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Signal Processing Solutions for the Networked Battlespace

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2014 48th Asilomar Conference on Signals, Systems and Computers

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