Picture of person typing on laptop with programming code visible on the laptop screen

World class computing and information science research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

The Department also includes the iSchool Research Group, which performs leading research into socio-technical phenomena and topics such as information retrieval and information seeking behaviour.


An approximate polynomial matrix eigenvalue decomposition algorithm for para-hermitian matrices

Redif, Soydan and Weiss, Stephan and McWhirter, John G. (2011) An approximate polynomial matrix eigenvalue decomposition algorithm for para-hermitian matrices. In: Proceedings of IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2011. IEEE, New York, pp. 421-425. ISBN 9781467307529

Full text not available in this repository. Request a copy from the Strathclyde author


In this paper, we propose an algorithm for computing an approximate polynomial matrix eigenvalue decomposition (PEVD). The PEVD of a para-Hermitian matrix yields a factorisation into a polynomial matrix product consisting of a spectrally majorised diagonal matrix that is pre- and post-multiplied by paraunitary (PU) matrices. All current PEVD algorithms, such as the second order sequential best rotation (SBR2) algorithm, perform a factorisation whereby diagonalisation and spectral majorisation are only achieved in approximation. The purpose of this paper is to present a new iterative approach which constitutes a “Householder-like” version of SBR2 and is akin to Tkacenko's approximate EVD (AEVD); however, unlike the AEVD, the proposed method carries out the diagonalisation successively by applying arbitrary-degree, finite impulse response PU matrices. We show an application of our algorithm to the design of signal-adapted PU filter banks for subband coding. Simulation results for the proposed approach show very close agreement with the behaviour of the infinite order principal component filter banks and demonstrate its superiority compared to state-of-the-art algorithms in terms of strong decorrelation and spectral majorisation.