Sequential matrix diagonalization algorithms for polynomial EVD of parahermitian matrices

S Redif, S Weiss, JG McWhirter - IEEE Transactions on Signal …, 2014 - ieeexplore.ieee.org
For parahermitian polynomial matrices, which can be used, for example, to characterize
space-time covariance in broadband array processing, the conventional eigenvalue …

Eigenvalue decomposition of a parahermitian matrix: Extraction of analytic eigenvalues

S Weiss, IK Proudler, FK Coutts - IEEE Transactions on Signal …, 2021 - ieeexplore.ieee.org
An analytic parahermitian matrix admits an eigenvalue decomposition (EVD) with analytic
eigenvalues and eigenvectors except in the case of multiplexed data. In this paper, we …

On the existence and uniqueness of the eigenvalue decomposition of a parahermitian matrix

S Weiss, J Pestana, IK Proudler - IEEE Transactions on Signal …, 2018 - ieeexplore.ieee.org
This paper addresses the extension of the factorization of a Hermitian matrix by an
eigenvalue decomposition (EVD) to the case of a parahermitian matrix that is analytic at …

MVDR broadband beamforming using polynomial matrix techniques

S Weiss, S Bendoukha, A Alzin… - 2015 23rd European …, 2015 - ieeexplore.ieee.org
This paper presents initial progress on formulating minimum variance distortionless
response (MVDR) broadband beam-forming using a generalised sidelobe canceller (GSC) …

Row-shift corrected truncation of paraunitary matrices for PEVD algorithms

J Corr, K Thompson, S Weiss… - 2015 23rd European …, 2015 - ieeexplore.ieee.org
In this paper, we show that the paraunitary (PU) matrices that arise from the polynomial
eigenvalue decomposition (PEVD) of a parahermitian matrix are not unique. In particular …

Multiple shift maximum element sequential matrix diagonalisation for parahermitian matrices

J Corr, K Thompson, S Weiss… - … IEEE Workshop on …, 2014 - ieeexplore.ieee.org
A polynomial eigenvalue decomposition of paraher-mitian matrices can be calculated
approximately using iterative approaches such as the sequential matrix diagonalisation …

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

JA Foster, JG McWhirter, MR Davies… - IEEE Transactions on …, 2009 - ieeexplore.ieee.org
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 …

Compact order polynomial singular value decomposition of a matrix of analytic functions

MA Bakhit, FA Khattak, IK Proudler… - 2023 IEEE 9th …, 2023 - ieeexplore.ieee.org
This paper presents a novel method for calculating a compact order singular value
decomposition (SVD) of polynomial matrices, building upon the recently proven existence of …

Multiple shift second order sequential best rotation algorithm for polynomial matrix EVD

Z Wang, JG McWhirter, J Corr… - 2015 23rd European …, 2015 - ieeexplore.ieee.org
In this paper, we present an improved version of the second order sequential best rotation
algorithm (SBR2) for polynomial matrix eigenvalue decomposition of para-Hermitian …

Efficient implementation of iterative polynomial matrix evd algorithms exploiting structural redundancy and parallelisation

FK Coutts, IK Proudler, S Weiss - IEEE Transactions on Circuits …, 2019 - ieeexplore.ieee.org
A number of algorithms are capable of iteratively calculating a polynomial matrix eigenvalue
decomposition (PEVD), which is a generalisation of the EVD and will diagonalise a …