Extension of Power Method to Para-Hermitian Matrices: Polynomial Power Method

This document extends the idea of the power method to polynomial para-Hermitian matrices for the extraction of the principal analytic eigenpair. The proposed extension repeatedly multiplies a polynomial vector with a para-Hermitian matrix followed by an appropriate normalization in each iteration. To limit the order growth of the product vector, truncation is performed post-normalization in each iteration. The method is validated through simulation results over an ensemble of randomised para-Hermitian matrices and is shown to perform significantly better than state-of-the-art algorithms.