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求解一类复对称线性系统的广义AOR迭代法

李旭, 李瑞丰   

  1. 兰州理工大学应用数学系, 兰州 730050
  • 收稿日期:2022-05-01 出版日期:2022-09-14 发布日期:2022-09-09
  • 通讯作者: 李旭,Email:lixu@lut.edu.cn
  • 基金资助:
    国家自然科学基金(11501272)和甘肃省自然科学基金(20JR5RA464)资助.

李旭, 李瑞丰. 求解一类复对称线性系统的广义AOR迭代法[J]. 数值计算与计算机应用, 2022, 43(3): 295-306.

Li Xu, Li Ruifeng. GENERALIZED AOR ITERATION METHODS FOR SOLVING A CLASS OF COMPLEX SYMMETRIC LINEAR SYSTEMS[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(3): 295-306.

GENERALIZED AOR ITERATION METHODS FOR SOLVING A CLASS OF COMPLEX SYMMETRIC LINEAR SYSTEMS

Li Xu, Li Ruifeng   

  1. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
  • Received:2022-05-01 Online:2022-09-14 Published:2022-09-09
针对求解一类广义复对称线性系统,Salkuyeh等学者利用等价2×2块实值形式提出了一种广义SOR (GSOR)迭代法.为了进一步提高计算效率,本文建立一种含有两个参数的广义AOR (GAOR)迭代法.详细分析了该方法的收敛性,得到一个范围更广的收敛域.最后,通过两个数值算例验证了GAOR迭代法的可行性与高效性.
For solving a broad class of complex symmetric linear systems, Salkuyeh et al. proposed the generalized SOR (GSOR) iteration method by using the equivalent block two-by-two real value forms. In order to further improve the computational efficiency, a generalized AOR (GAOR) iteration method with two parameters is established in this paper. The convergence properties of the method are analyzed in detail and a wider convergence domain is obtained. The feasibility and efficiency of the GAOR iteration method are verified by two numerical examples.

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