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连续Sylvester方程的广义正定和反Hermitian分裂迭代法及其超松弛加速

李旭, 李明翔   

  1. 兰州理工大学应用数学系, 兰州 730050
  • 收稿日期:2019-09-22 出版日期:2021-08-15 发布日期:2021-08-20
  • 通讯作者: 李旭,Email:lixu@lut.edu.cn.
  • 基金资助:
    国家自然科学基金(11501272)资助.

李旭, 李明翔. 连续Sylvester方程的广义正定和反Hermitian分裂迭代法及其超松弛加速[J]. 计算数学, 2021, 43(3): 354-366.

Li Xu, Li Mingxiang. GENERALIZED POSITIVE-DEFINITE AND SKEW-HERMITIAN SPLITTING ITERATION METHOD AND ITS SOR ACCELERATION FOR CONTINUOUS SYLVESTER EQUATIONS[J]. Mathematica Numerica Sinica, 2021, 43(3): 354-366.

GENERALIZED POSITIVE-DEFINITE AND SKEW-HERMITIAN SPLITTING ITERATION METHOD AND ITS SOR ACCELERATION FOR CONTINUOUS SYLVESTER EQUATIONS

Li Xu, Li Mingxiang   

  1. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
  • Received:2019-09-22 Online:2021-08-15 Published:2021-08-20
对于求解大型稀疏连续Sylvester方程,Bai提出了非常有效的Hermitian和反Hermitian分裂(HSS)迭代法.为了进一步提高求解这类方程的效率,本文建立一种广义正定和反Hermitian分裂(GPSS)迭代法,并且提出不精确GPSS(IGPSS)迭代法从而可以降低计算成本.对GPSS迭代法及其不精确变体的收敛性作了详细分析.另外,建立一种超松弛加速GPSS(AGPSS)方法并且讨论了收敛性.数值结果表明了方法的高效性和鲁棒性.
Bai proposed an efficient Hermitian and skew-Hermitian splitting (HSS) iteration method for solving a broad class of large sparse continuous Sylvester equations. To further improve the efficiency, in this paper we present a generalized positive-definite and skew-Hermitian splitting (GPSS) iteration method for this matrix equation. Then we establish the inexact variant of the GPSS (IGPSS) iteration method which can reduce the computational cost. Convergence properties of the GPSS iteration method and its inexact variant are analyzed in detail. Moreover, an SOR accelerated GPSS (AGPSS) method is established and its convergence behavior is discussed. Numerical results illustrate the efficiency and robustness of our methods.

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