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An algorithm for calculating the QR and singular value decompositions of polynomial matrices

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journal contribution
posted on 2010-02-16, 16:00 authored by Joanne Foster, John McWhirter, Martin Davies, Jonathon Chambers
In this paper, a new algorithm for calculating the QR decomposition (QRD) of a polynomial matrix is introduced. This algorithm amounts to transforming a polynomial matrix to upper triangular form by application of a series of paraunitary matrices such as elementary delay and rotation matrices. It is shown that this algorithm can also be used to formulate the singular value decomposition (SVD) of a polynomial matrix, which essentially amounts to diagonalizing a polynomial matrix again by application of a series of paraunitary matrices. Example matrices are used to demonstrate both types of decomposition. Mathematical proofs of convergence of both decompositions are also outlined. Finally, a possible application of such decompositions in multichannel signal processing is discussed.

History

School

  • Mechanical, Electrical and Manufacturing Engineering

Citation

FOSTER, J....et al., 2009. An algorithm for calculating the QR and singular value decompositions of polynomial matrices. IEEE Transactions on Signal Processing, 58(3), pp. 1263-1274.

Publisher

© IEEE

Version

  • AM (Accepted Manuscript)

Publication date

2009

Notes

This article was published in the journal IEEE Transactions on Signal Processing [© IEEE] and is also available at: http://ieeexplore.ieee.org/. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

ISSN

1053-587X

Language

  • en