The Condition numbers are defined for the stabilizing Solutions of Continuoustime, discrete-time and the reverse discrete-time algebraic Riccati equations. The first-order perturbation expansions for the stabilizing S...The Condition numbers are defined for the stabilizing Solutions of Continuoustime, discrete-time and the reverse discrete-time algebraic Riccati equations. The first-order perturbation expansions for the stabilizing Solutions are also obtained.展开更多
In this paper we consider domain decomposition methods with Lagrangian multipliers, which are applied to solving parabolic problems. We shall estimate condition numbers of the resulting interface matrices, and constru...In this paper we consider domain decomposition methods with Lagrangian multipliers, which are applied to solving parabolic problems. We shall estimate condition numbers of the resulting interface matrices, and construct two kinds of simple preconditioners for the corresponding interface equations. It will be shown that the condition numbers of the resulting preconditioned interface matrices are almost optimal.展开更多
The convergence of the entropy function method for convex nonlinear min-maxproblems is proved. By analyzing the eigenvalue structure of the Hessian matrix,it is found that for high values of the approximation controll...The convergence of the entropy function method for convex nonlinear min-maxproblems is proved. By analyzing the eigenvalue structure of the Hessian matrix,it is found that for high values of the approximation controlling parameter c thedifferentiable optimization problem involved in the entropy function method becomes ill-conditioned and hence difficult to solve. Furthermore, it is shown thatthe entropy function method is indeed equivalent to the simple exponential penaltymethod and hence can be further discussed in the framework of penalty functionmethods. Based on this discovery, in the convex case, it is proved that the entropyfunction method involving Lagrange multiplier (i.e. exponential multiplier penaltymethod) is convergence for ally finite parameter c and hence the ill-condition encountered in the original method can be completely avoided.展开更多
文摘The Condition numbers are defined for the stabilizing Solutions of Continuoustime, discrete-time and the reverse discrete-time algebraic Riccati equations. The first-order perturbation expansions for the stabilizing Solutions are also obtained.
文摘In this paper we consider domain decomposition methods with Lagrangian multipliers, which are applied to solving parabolic problems. We shall estimate condition numbers of the resulting interface matrices, and construct two kinds of simple preconditioners for the corresponding interface equations. It will be shown that the condition numbers of the resulting preconditioned interface matrices are almost optimal.
文摘The convergence of the entropy function method for convex nonlinear min-maxproblems is proved. By analyzing the eigenvalue structure of the Hessian matrix,it is found that for high values of the approximation controlling parameter c thedifferentiable optimization problem involved in the entropy function method becomes ill-conditioned and hence difficult to solve. Furthermore, it is shown thatthe entropy function method is indeed equivalent to the simple exponential penaltymethod and hence can be further discussed in the framework of penalty functionmethods. Based on this discovery, in the convex case, it is proved that the entropyfunction method involving Lagrange multiplier (i.e. exponential multiplier penaltymethod) is convergence for ally finite parameter c and hence the ill-condition encountered in the original method can be completely avoided.
