SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 306-326, March 2024.
Abstract. This paper considers a novel structure-preserving method for solving non-Hermitian quaternion linear systems arising from color image deblurred problems. From the quaternion Lanczos biorthogonalization procedure that preserves the quaternion tridiagonal form at each iteration, we derive the quaternion biconjugate gradient method for solving the linear systems and then establish the convergence analysis of the proposed algorithm. Finally, we provide some numerical examples to illustrate the feasibility and validity of our method in comparison with the QGMRES, especially in terms of computing time.

中文翻译：

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结构保持四元数双共轭梯度法

《SIAM 矩阵分析与应用杂志》，第 45 卷，第 1 期，第 306-326 页，2024 年 3 月。
摘要。本文考虑了一种新颖的结构保持方法，用于解决由彩色图像去模糊问题引起的非厄米四元数线性系统。从每次迭代时保留四元数三对角形式的四元数 Lanczos 双正交化过程中，我们推导出用于求解线性系统的四元数双共轭梯度法，然后建立所提出算法的收敛性分析。最后，我们提供了一些数值例子来说明我们的方法与 QGMRES 相比的可行性和有效性，特别是在计算时间方面。