This paper further extends the shift-splitting(SS)and local shift-splitting(LSS)preconditioners to solve the general block two-by-two linear systems.We demonstrate that the eigenvalues of the corresponding preconditio...This paper further extends the shift-splitting(SS)and local shift-splitting(LSS)preconditioners to solve the general block two-by-two linear systems.We demonstrate that the eigenvalues of the corresponding preconditioned matrices cluster tightly around 2 by detailed spectral property analysis.Numerical experiments not only validate the theoretical results but also show the effectiveness and superiority of the SS and LSS preconditioners by comparing them with some existing preconditioners applied to the generalized minimal residual(GMRES)method for solving the block two-by-two linear systems.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2023 autonomous region full-time introduction of high-level talent research project(Grant No.2023BSB03036)2024 higher education science research project of the education department of the autonomous region(NYG2024055).
文摘This paper further extends the shift-splitting(SS)and local shift-splitting(LSS)preconditioners to solve the general block two-by-two linear systems.We demonstrate that the eigenvalues of the corresponding preconditioned matrices cluster tightly around 2 by detailed spectral property analysis.Numerical experiments not only validate the theoretical results but also show the effectiveness and superiority of the SS and LSS preconditioners by comparing them with some existing preconditioners applied to the generalized minimal residual(GMRES)method for solving the block two-by-two linear systems.
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.
