On Eigenvector Computation and Eigenvalue Reordering for the Non-Hermitian Quaternion Eigenvalue Problem

TL;DR

This paper extends the quaternion QR algorithm by introducing eigenvector computation and eigenvalue reordering methods, successfully applying aggressive early deflation to improve convergence in quaternion eigenvalue problems.

Contribution

It presents new algorithms for eigenvector computation and eigenvalue reordering specifically tailored for the quaternion QR algorithm, including the application of AED.

Findings

Algorithms demonstrate improved convergence

Effective eigenvalue reordering achieved

Numerical experiments confirm efficiency

Abstract

In this paper we present several additions to the quaternion QR algorithm, including algorithms for eigenvector computation and eigenvalue reordering. A key outcome of the eigenvalue reordering algorithm is that the aggressive early deflation (AED) technique, which significantly enhances the convergence of the QR algorithm, is successfully applied to the quaternion eigenvalue problem. We conduct numerical experiments to demonstrate the efficiency and effectiveness of the proposed algorithms.