求解四元数矩阵方程AX+XB=C的全局拟极小残量法

doi:10.6040/j.issn.1671-9352.0.2023.456

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (12): 66-74.doi: 10.6040/j.issn.1671-9352.0.2023.456

求解四元数矩阵方程AX+XB=C的全局拟极小残量法

吴玉玲¹,郑佳莉¹,柯艺芬^1,2,3*,许小芳¹

1.福建师范大学数学与统计学院, 福建福州 350117;2.福建师范大学分析数学及应用教育部重点实验室, 福建福州 350117;3.福建省应用数学中心, 福建福州 350117

发布日期:2025-12-10
通讯作者: 柯艺芬(1989— ),女,副研究员,博士,研究方向为数值代数及其应用. E-mail:keyifen@fjnu.edu.cn
作者简介:吴玉玲(1999— ),女,硕士研究生,研究方向为数值代数及其应用. E-mail:wuyl0310@163.com*通信作者:柯艺芬(1989— ),女,副研究员,博士,研究方向为数值代数及其应用. E-mail:keyifen@fjnu.edu.cn
基金资助:
国家自然科学基金资助项目(12371378,11901098);福建省自然科学基金项目(2023J011127,2023J01955,2020J05034)

Global quasi-minimal residual method for solving quaternion matrix equation AX+XB=C

WU Yuling¹, ZHENG Jiali¹, KE Yifen^1,2,3*, XU Xiaofang¹

1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, Fujian, China;
2. Key Laboratory of Analytical Mathematical and Applications(Ministry of Education), Fujian Normal University, Fuzhou 350117, Fujian, China;
3. Center for Applied Mathematics of Fujian province(FJNU), Fuzhou 350117, Fujian, China

Published:2025-12-10

摘要/Abstract

摘要： 提出四元数体上的非对称Lanczos方法,基于此,给出求解Sylvester四元数矩阵方程AX+XB=C的全局四元数拟极小残量法。该方法能够有效降低算法执行过程中的存储空间,进一步,通过数值算例验证所提算法的可行性和有效性。

关键词: 四元数, Sylvester矩阵方程, 非对称Lanczos方法, 全局四元数拟极小残量法

Abstract: In this paper, the quaternion nonsymmetric Lanczos method is proposed. Based on this method, the global quaternion quasi-minimum residual method is established for solving the Sylvester quaternion matrix equation AX+XB=C, which can effectively reduce the storage space during algorithm execution. Further, some numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.

Key words: quaternion, Sylvester matrix equation, nonsymmetric Lanczos method, global quaternion quasi-minimal residual method

中图分类号:

O241

吴玉玲,郑佳莉,柯艺芬,许小芳. 求解四元数矩阵方程AX+XB=C的全局拟极小残量法[J]. 《山东大学学报(理学版)》, 2025, 60(12): 66-74.

WU Yuling, ZHENG Jiali, KE Yifen, XU Xiaofang. Global quasi-minimal residual method for solving quaternion matrix equation AX+XB=C[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 66-74.

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求解四元数矩阵方程AX+XB=C的全局拟极小残量法

Global quasi-minimal residual method for solving quaternion matrix equation AX+XB=C

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