白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂(HSS)迭代方法(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methodsfor non-Hermitian positive definite linear systems.SIAM J.Matrix A...白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂(HSS)迭代方法(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methodsfor non-Hermitian positive definite linear systems.SIAM J.Matrix Anal.Appl.,2003,24:603-626).本文精确地估计了用HSS迭代方法求解广义鞍点问题时在加权2-范数和2-范数下的收缩因子.在实际的计算中,正是这些收缩因子而不是迭代矩阵的谱半径,本质上控制着HSS迭代方法的实际收敛速度.根据文中的分析,求解广义鞍点问题的HSS迭代方法的收缩因子在加权2-范数下等于1,在2-范数下它会大于等于1,而在某种适当选取的范数之下,它则会小于1.最后,用数值算例说明了理论结果的正确性.展开更多
提出了求解广义Lyapunov方程的HSS(Hermitian and skew-Hermitian splitting)迭代法,分析了该方法的收敛性,给出了收敛因子的上界.为了降低HSS迭代法的计算量,提出了求解广义Lyapunov方程的非精确HSS迭代法,并分析其收敛性.数值结果表明...提出了求解广义Lyapunov方程的HSS(Hermitian and skew-Hermitian splitting)迭代法,分析了该方法的收敛性,给出了收敛因子的上界.为了降低HSS迭代法的计算量,提出了求解广义Lyapunov方程的非精确HSS迭代法,并分析其收敛性.数值结果表明,求解广义Lyapunov方程的HSS迭代法及非精确HSS迭代法是有效的.展开更多
Recently,some authors(Shen and Shi,2016)studied the generalized shiftsplitting(GSS)iteration method for singular saddle point problem with nonsymmetric positive definite(1,1)-block and symmetric positive semidefinite(...Recently,some authors(Shen and Shi,2016)studied the generalized shiftsplitting(GSS)iteration method for singular saddle point problem with nonsymmetric positive definite(1,1)-block and symmetric positive semidefinite(2,2)-block.In this paper,we further apply the GSS iteration method to solve singular saddle point problem with nonsymmetric positive semidefinite(1,1)-block and symmetric positive semidefinite(2,2)-block,prove the semi-convergence of the GSS iteration method and analyze the spectral properties of the corresponding preconditioned matrix.Numerical experiment is given to indicate that the GSS iteration method with appropriate iteration parameters is effective and competitive for practical use.展开更多
基金Project supported by the State Key Laboratory of Scientific/Engineering Computing,Chinese Academy of Sciencesthe International Science and Technology Cooperation Program of China(2010DFA14700)the National Natural Science Foundation of China(11071192)
文摘白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂(HSS)迭代方法(Bai Z Z,Golub G H,Ng M K.Hermitian and skew-Hermitian splitting methodsfor non-Hermitian positive definite linear systems.SIAM J.Matrix Anal.Appl.,2003,24:603-626).本文精确地估计了用HSS迭代方法求解广义鞍点问题时在加权2-范数和2-范数下的收缩因子.在实际的计算中,正是这些收缩因子而不是迭代矩阵的谱半径,本质上控制着HSS迭代方法的实际收敛速度.根据文中的分析,求解广义鞍点问题的HSS迭代方法的收缩因子在加权2-范数下等于1,在2-范数下它会大于等于1,而在某种适当选取的范数之下,它则会小于1.最后,用数值算例说明了理论结果的正确性.
文摘提出了求解广义Lyapunov方程的HSS(Hermitian and skew-Hermitian splitting)迭代法,分析了该方法的收敛性,给出了收敛因子的上界.为了降低HSS迭代法的计算量,提出了求解广义Lyapunov方程的非精确HSS迭代法,并分析其收敛性.数值结果表明,求解广义Lyapunov方程的HSS迭代法及非精确HSS迭代法是有效的.
基金Supported by Guangxi Science and Technology Department Specific Research Project of Guangxi for Research Bases and Talents(Grant No.GHIKE-AD23023001)Natural Science Foundation of Guangxi Minzu University(Grant No.2021KJQD01)Xiangsi Lake Young Scholars Innovation Team of Guangxi University for Nationalities(Grant No.2021RSCXSHQN05)。
文摘Recently,some authors(Shen and Shi,2016)studied the generalized shiftsplitting(GSS)iteration method for singular saddle point problem with nonsymmetric positive definite(1,1)-block and symmetric positive semidefinite(2,2)-block.In this paper,we further apply the GSS iteration method to solve singular saddle point problem with nonsymmetric positive semidefinite(1,1)-block and symmetric positive semidefinite(2,2)-block,prove the semi-convergence of the GSS iteration method and analyze the spectral properties of the corresponding preconditioned matrix.Numerical experiment is given to indicate that the GSS iteration method with appropriate iteration parameters is effective and competitive for practical use.
