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

Zhigang Jia; Meiyue Shao; Yanjun Shao

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arXiv · 2511.02232

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

Zhigang Jia·Meiyue Shao·Yanjun Shao

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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.

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Zhigang Jia, Meiyue Shao, Yanjun Shao. 2025-11-04. On Eigenvector Computation and Eigenvalue Reordering for the Non-Hermitian Quaternion Eigenvalue Problem. https://arxiv.org/abs/2511.02232

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