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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (3): 481-493.doi: 10.3969/j.issn.1005-3085.2024.03.008

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连续Sylvester矩阵方程的参数化单步HSS迭代法

马昌凤   

  1. 福州外语外贸学院大数据学院数据科学与智能计算重点实验室，福州 350202
  • 收稿日期:2022-01-14 接受日期:2022-05-16 出版日期:2024-06-15 发布日期:2024-08-15
  • 基金资助:
    国家自然科学基金(12371378)；福建省重大教改项目(FBJG20200310)；福建省新工科研究实践项目(J1593419745784GS).

A Parameterized Single-step HSS Iteration Method for Continuous Sylvester Matrix Equations

MA Changfeng   

  1. School of Big Data & Key Laboratory of Data Science and Intelligent Computing, Fuzhou University of International Studies and Trade, Fuzhou 350202
  • Received:2022-01-14 Accepted:2022-05-16 Online:2024-06-15 Published:2024-08-15
  • Supported by:
    The National Natural Science Foundation of China (12371378); the Major Educational Reform Project of Fujian Province (FBJG20200310); the New Engineering Research Practice Project (J1593419745784GS).

摘要： 对连续Sylvester矩阵方程的数值算法进行了深入研究，并创新性地提出了一种参数化单步HSS迭代方法。该方法具有独特的求解思路，并证明了其收敛性。为提升性能，通过最小化迭代矩阵谱半径上界寻找拟最优参数。数值实验验证了新方法的有效性和稳健性，展示了其在求解连续Sylvester矩阵方程时的高效和稳定，为相关数值计算提供新工具。

关键词: 连续Sylvester矩阵方程, PSHSS迭代法, 收敛性分析, 数值实验

Abstract: The numerical algorithm of continuous Sylvester matrix equation is studied deeply, and a parameterized single step HSS iteration method is proposed innovatively. This method has a unique solution idea and its convergence is proved. In order to improve the performance, quasi-optimal parameters are found by minimizing the upper bound of the spectral radius of the iterative matrix. Numerical experiments verify the effectiveness and robustness of the new method, and demonstrate its high efficiency and stability in solving continuous Sylvester matrix equations, which provides a new tool for relevant numerical calculation.

Key words: continuous Sylvester equation, PSHSS iteration method, convergence analysis, numerical experiments

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