Scalable analytic eigenvalue extraction from a parahermitian matrix

In order to extract the analytic eigenvalues from a parahermitian matrix, the computational cost of the current state-of-the-art method grows factorially with the matrix dimension. Even though the approach offers benefits such as proven convergence, it has been found impractical to operate on matrices with a spatial dimension great than four. Evaluated in the discrete Fourier transform (DFT) domain, the computational bottleneck of this method is a maximum likelihood sequence (MLS) estimation, which probes a set of paths of likely associations across DFT bins, and only retains the best of these. In this paper, we investigate an algorithm that remains covered by the existing method's proof of convergence but results in a significant reduction in computation cost by trading the number of retained paths against the DFT length. We motivate this, and also introduce an enhanced initialisation point for the MLS estimation. We illustrate the benefits of scalable analytic extraction algorithm in a number of simulations.