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

2025/11/04 by Jia, Zhigang, Shao, Meiyue, Shao, Yanjun
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2511.02232

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

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.

Citations

• On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication

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