### 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 language | English |
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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 |
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Abbreviated title | CAMSAP |

Country | Netherlands Antilles |

City | Curacao |

Period | 10/12/17 → 13/12/17 |

Internet address |

### Keywords

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

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## 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.