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Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms

Coutts, Fraser K. and Corr, Jamie and Thompson, Keith and Weiss, Stephan and Proudler, Ian K. and McWhirter, John G. (2016) Memory and complexity reduction in parahermitian matrix manipulations of PEVD algorithms. In: 2016 24th European Signal Processing Conference. IEEE, Piscataway, pp. 1633-1637. ISBN 9780992862657

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A number of algorithms for the iterative calculation of a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. This paper addresses savings — both computationally and in terms of memory use — that exploit the parahermitian structure of the matrix being decomposed, and also suggests an implicit trimming approach to efficiently curb the polynomial order growth usually observed during iterations of the PEVD algorithms. We demonstrate that with the proposed techniques, both storage and computations can be significantly reduced, impacting on a number of broadband multichannel problems.