A comparison of iterative and DFT-based polynomial matrix eigenvalue decompositions

Research output: Contribution to conferencePaper

Abstract

A variety of algorithms have been developed to compute an approximate polynomial matrix eigenvalue decomposition (PEVD). As an extension of the ordinary EVD to polynomial matrices, the PEVD will generate paraunitary matrices that diagonalise a parahermitian matrix. This paper compares the decomposition accuracies of two fundamentally different methods capable of computing an approximate PEVD. The first of these --- sequential matrix diagonalisation (SMD) --- iteratively decomposes a parahermitian matrix, while the second DFT-based algorithm computes a pointwise in frequency decomposition. We demonstrate through the use of examples that both algorithms can achieve varying levels of decomposition accuracy, and provide results that indicate the type of broadband multichannel problems that are better suited to each algorithm. It is shown that iterative methods, which generate paraunitary eigenvectors, are suited for general applications with a low number of sensors, while a DFT-based approach is useful for fixed, finite order decompositions with a small number of lags.

Conference

ConferenceIEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Abbreviated titleCAMSAP
CountryNetherlands Antilles
CityCuracao
Period10/12/1713/12/17
Internet address

Fingerprint

Discrete Fourier transforms
Polynomials
Decomposition
Iterative methods
Eigenvalues and eigenfunctions
Sensors

Keywords

  • polynomial matrix eigenvalue decompositions
  • PEVD
  • sequential matrix diagonalisation
  • SMD
  • broadband multichannel problems

Cite this

Coutts, F. K., Thompson, K., Proudler, I. K., & Weiss, S. (2017). A comparison of iterative and DFT-based polynomial matrix eigenvalue decompositions. Paper presented at IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Curacao, Netherlands Antilles.
Coutts, Fraser K. ; Thompson, Keith ; Proudler, Ian K. ; Weiss, Stephan. / A comparison of iterative and DFT-based polynomial matrix eigenvalue decompositions. Paper presented at IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Curacao, Netherlands Antilles.5 p.
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abstract = "A variety of algorithms have been developed to compute an approximate polynomial matrix eigenvalue decomposition (PEVD). As an extension of the ordinary EVD to polynomial matrices, the PEVD will generate paraunitary matrices that diagonalise a parahermitian matrix. This paper compares the decomposition accuracies of two fundamentally different methods capable of computing an approximate PEVD. The first of these --- sequential matrix diagonalisation (SMD) --- iteratively decomposes a parahermitian matrix, while the second DFT-based algorithm computes a pointwise in frequency decomposition. We demonstrate through the use of examples that both algorithms can achieve varying levels of decomposition accuracy, and provide results that indicate the type of broadband multichannel problems that are better suited to each algorithm. It is shown that iterative methods, which generate paraunitary eigenvectors, are suited for general applications with a low number of sensors, while a DFT-based approach is useful for fixed, finite order decompositions with a small number of lags.",
keywords = "polynomial matrix eigenvalue decompositions, PEVD, sequential matrix diagonalisation, SMD, broadband multichannel problems",
author = "Coutts, {Fraser K.} and Keith Thompson and Proudler, {Ian K.} and Stephan Weiss",
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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Coutts, FK, Thompson, K, Proudler, IK & Weiss, S 2017, 'A comparison of iterative and DFT-based polynomial matrix eigenvalue decompositions' Paper presented at IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Curacao, Netherlands Antilles, 10/12/17 - 13/12/17, .

A comparison of iterative and DFT-based polynomial matrix eigenvalue decompositions. / Coutts, Fraser K.; Thompson, Keith; Proudler, Ian K.; Weiss, Stephan.

2017. Paper presented at IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Curacao, Netherlands Antilles.

Research output: Contribution to conferencePaper

TY - CONF

T1 - A comparison of iterative and DFT-based polynomial matrix eigenvalue decompositions

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

Y1 - 2017/12/10

N2 - A variety of algorithms have been developed to compute an approximate polynomial matrix eigenvalue decomposition (PEVD). As an extension of the ordinary EVD to polynomial matrices, the PEVD will generate paraunitary matrices that diagonalise a parahermitian matrix. This paper compares the decomposition accuracies of two fundamentally different methods capable of computing an approximate PEVD. The first of these --- sequential matrix diagonalisation (SMD) --- iteratively decomposes a parahermitian matrix, while the second DFT-based algorithm computes a pointwise in frequency decomposition. We demonstrate through the use of examples that both algorithms can achieve varying levels of decomposition accuracy, and provide results that indicate the type of broadband multichannel problems that are better suited to each algorithm. It is shown that iterative methods, which generate paraunitary eigenvectors, are suited for general applications with a low number of sensors, while a DFT-based approach is useful for fixed, finite order decompositions with a small number of lags.

AB - A variety of algorithms have been developed to compute an approximate polynomial matrix eigenvalue decomposition (PEVD). As an extension of the ordinary EVD to polynomial matrices, the PEVD will generate paraunitary matrices that diagonalise a parahermitian matrix. This paper compares the decomposition accuracies of two fundamentally different methods capable of computing an approximate PEVD. The first of these --- sequential matrix diagonalisation (SMD) --- iteratively decomposes a parahermitian matrix, while the second DFT-based algorithm computes a pointwise in frequency decomposition. We demonstrate through the use of examples that both algorithms can achieve varying levels of decomposition accuracy, and provide results that indicate the type of broadband multichannel problems that are better suited to each algorithm. It is shown that iterative methods, which generate paraunitary eigenvectors, are suited for general applications with a low number of sensors, while a DFT-based approach is useful for fixed, finite order decompositions with a small number of lags.

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Coutts FK, Thompson K, Proudler IK, Weiss S. A comparison of iterative and DFT-based polynomial matrix eigenvalue decompositions. 2017. Paper presented at IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Curacao, Netherlands Antilles.