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

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

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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.
Original languageEnglish
Number of pages5
Publication statusPublished - 10 Dec 2017
EventIEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Curacao, Netherlands Antilles
Duration: 10 Dec 201713 Dec 2017
http://www.cs.huji.ac.il/conferences/CAMSAP17/

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

Keywords

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

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    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.