In recent years,many efforts have been made to numerically solving the constrained optimization distributed control problems,in which the most common one is to discretize the partial differential equation first and th...In recent years,many efforts have been made to numerically solving the constrained optimization distributed control problems,in which the most common one is to discretize the partial differential equation first and then solve the resulting system of linear equations.A number of preconditioned Krylov subspace methods have been constructed to solve the resulting system of linear equations in the literature.In this paper,by analyzing the block-diagonal preconditioner presented by Zhang,et al.(Zhang X Y,Yan H Y,Huang Y M.On preconditioned MINRES method for solving the distributed control problems.Commun Appl Math Comput,2014,28:128-132.),we propose a parameterized block-diagonally preconditioned linear system where a parameterized preconditioner is utilized and the preconditioned MINRES method is applied to solve the system of linear equations.The spectral analysis of the proposed preconditioned matrix shows that the spectral distribution of the parameterized preconditioning matrix should be much more clustered if the parameter is greater than 1.Numerical Experiments show that the preconditioned MINRES method is efficient for solving the distributed control problems.展开更多
基金Project supported by the National Natural Science Foundation of China(11571156)
文摘In recent years,many efforts have been made to numerically solving the constrained optimization distributed control problems,in which the most common one is to discretize the partial differential equation first and then solve the resulting system of linear equations.A number of preconditioned Krylov subspace methods have been constructed to solve the resulting system of linear equations in the literature.In this paper,by analyzing the block-diagonal preconditioner presented by Zhang,et al.(Zhang X Y,Yan H Y,Huang Y M.On preconditioned MINRES method for solving the distributed control problems.Commun Appl Math Comput,2014,28:128-132.),we propose a parameterized block-diagonally preconditioned linear system where a parameterized preconditioner is utilized and the preconditioned MINRES method is applied to solve the system of linear equations.The spectral analysis of the proposed preconditioned matrix shows that the spectral distribution of the parameterized preconditioning matrix should be much more clustered if the parameter is greater than 1.Numerical Experiments show that the preconditioned MINRES method is efficient for solving the distributed control problems.
