Restricted update sequential matrix diagonalisation for parahermitian matrices

Fraser K. Coutts; Keith Thompson; Ian K. Proudler; Stephan Weiss

Restricted update sequential matrix diagonalisation for parahermitian matrices

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

Electronic And Electrical Engineering

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Abstract

A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations. This paper introduces a novel restricted update approach for the sequential matrix diagonalisation (SMD) PEVD algorithm, which can be implemented with minimal impact on algorithm accuracy and convergence. We demonstrate that by using the proposed restricted update SMD (RU-SMD) algorithm instead of SMD, PEVD complexity and execution time can be significantly reduced. This reduction impacts on a number of broadband multichannel problems.

Original language	English
Number of pages	5
Publication status	Published - 10 Dec 2017
Event	IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Curacao, Netherlands Antilles Duration: 10 Dec 2017 → 13 Dec 2017 http://www.cs.huji.ac.il/conferences/CAMSAP17/

Conference

Conference	IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Abbreviated title	CAMSAP
Country/Territory	Netherlands Antilles
City	Curacao
Period	10/12/17 → 13/12/17
Internet address	http://www.cs.huji.ac.il/conferences/CAMSAP17/

Keywords

polynomial matrix eigenvalue decompositions
PEVD
polynomial matrices
parahermitian matrices
broadband multichannel problems

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Coutts-etal-CAMSAP-2017-Restricted-update-sequential-matrix-diagonalisation-for-parahermitian-matricesAccepted author manuscript, 182 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

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title = "Restricted update sequential matrix diagonalisation for parahermitian matrices",

abstract = "A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations. This paper introduces a novel restricted update approach for the sequential matrix diagonalisation (SMD) PEVD algorithm, which can be implemented with minimal impact on algorithm accuracy and convergence. We demonstrate that by using the proposed restricted update SMD (RU-SMD) algorithm instead of SMD, PEVD complexity and execution time can be significantly reduced. This reduction impacts on a number of broadband multichannel problems.",

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note = "(c) 2017 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.; IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP ; Conference date: 10-12-2017 Through 13-12-2017",

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AU - Coutts, Fraser K.

AU - Thompson, Keith

AU - Proudler, Ian K.

AU - Weiss, Stephan

N1 - (c) 2017 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 - 2017/12/10

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N2 - A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations. This paper introduces a novel restricted update approach for the sequential matrix diagonalisation (SMD) PEVD algorithm, which can be implemented with minimal impact on algorithm accuracy and convergence. We demonstrate that by using the proposed restricted update SMD (RU-SMD) algorithm instead of SMD, PEVD complexity and execution time can be significantly reduced. This reduction impacts on a number of broadband multichannel problems.

AB - A number of algorithms capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is an extension of the ordinary EVD to polynomial matrices and will diagonalise a parahermitian matrix using paraunitary operations. This paper introduces a novel restricted update approach for the sequential matrix diagonalisation (SMD) PEVD algorithm, which can be implemented with minimal impact on algorithm accuracy and convergence. We demonstrate that by using the proposed restricted update SMD (RU-SMD) algorithm instead of SMD, PEVD complexity and execution time can be significantly reduced. This reduction impacts on a number of broadband multichannel problems.

KW - polynomial matrix eigenvalue decompositions

KW - PEVD

KW - polynomial matrices

KW - parahermitian matrices

KW - broadband multichannel problems

M3 - Paper

T2 - IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing

Y2 - 10 December 2017 through 13 December 2017

ER -

Restricted update sequential matrix diagonalisation for parahermitian matrices

Abstract

Conference

Keywords

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Signal Processing Solutions for the Networked Battlespace

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