Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices

Coutts, Fraser K. and Corr, Jamie and Thompson, Keith and Proudler, Ian K. and Weiss, Stephan (2017) Divide-and-conquer sequential matrix diagonalisation for parahermitian matrices. In: IEEE Sensor Signal Processing in Defence Conference, 2017-12-06 - 2017-12-07, London. (In Press)

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    Abstract

    A number of algorithms capable of iteratively calculating 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. Inspired by the existence of low complexity divide-and-conquer solutions to eigenproblems, this paper addresses a divide-and-conquer approach to the PEVD utilising the sequential matrix diagonalisation (SMD) algorithm. We demonstrate that with the proposed techniques, encapsulated in a novel algorithm titled divide-and-conquer sequential matrix diagonalisation (DC-SMD), algorithm complexity can be significantly reduced. This reduction impacts on a number of broadband multichannel problems, including those involving large arrays.