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Cyclic-by-row approximation of iterative polynomial EVD algorithms

Corr, Jamie and Thompson, Keith and Weiss, Stephan and McWhirter, John G. and Proudler, Ian K. (2014) Cyclic-by-row approximation of iterative polynomial EVD algorithms. In: Sensor Signal Processing for Defence (SSPD), 2014. IEEE, pp. 1-5. ISBN 978-1-4799-5294-6

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Abstract

A recent class of sequential matrix diagonalisation (SMD) algorithms have been demonstrated to provide a fast converging solution to iteratively approximating the polynomial eigenvalue decomposition of a parahermitian matrix. However, the calculation of an EVD, and the application of a full unitary matrix to every time lag of the parahermitian matrix in the SMD algorithm results in a high numerical cost. In this paper, we replace the EVD with a limited number of Givens rotations forming a cyclic-by-row Jacobi sweep. Simulations indicate that a considerable reduction in computational complexity compared to SMD can be achieved with a negligible sacrifice in diagonalisation performance, such that the benefits in applying the SMD are maintained.