集值映射向量最优化的最优性条件

本文在序线性拓扑空间中,证明了广义Y+一次似凸集值映射的一个择一性定理,利用此定理,我们得到集值映射向量最优化问题的最优性条件.     

All Admissible Linear Estimators under Quadratic Loss in Multivariate Model

§ 1.Introduction and Notations　In this paper,for any given matrices A and B,A B denotes the Kronecker productof A and B,A is a vector formed by stacking the columns of A under each other,μ(A)is a space generated by the columns of A,and PA=A(A′A) - A′. Fourthmore,if A andB are square matrices,then A>B and A≥ B mean that A-B is a symmetrical positiveand nonnegative matrix,respectively,andλi(A) is the i-th largest eigenvalue of A.　Consider general multivariate linear modelY …     

交换主理想整环上立方幂等矩阵的线性保持

设Ｒ（≠Ｆ_３）是特征不为２的交换主理想整环,Ｍ_ｎ（Ｒ）定义Ｒ上的ｎ×ｎ矩阵模,本文刻划当ｎ≥ｍ时从Ｍ_ｎ（Ｒ）到Ｍ_ｎ（Ｒ）的保持立方幂等矩阵的线性映射的形式,由此推广了Ｃｈａｎ和Ｌｉｍ的一个结果（［１,定理３］）．     

Quasi-maximum likelihood estimators in generalized linear models with autoregressive processes

The paper studies a generalized linear model(GLM)y_t = h(x_t~T β) + ε_t,t = l,2,...,n,where ε_1 = η_1,ε_1 =ρε_t +η_t,t = 2,3,...;n,h is a continuous differentiable function,η_t's are independent and identically distributed random errors with zero mean and finite variance σ~2.Firstly,the quasi-maximum likelihood(QML) estimators of β,p and σ~2 are given.Secondly,under mild conditions,the asymptotic properties(including the existence,weak consistency and asymptotic distribution) of the QML estimators are investigated.Lastly,the validity of method is illuminated by a simulation example.     

ON AUGMENTED LAGRANGIAN METHODS FOR SADDLE-POINT LINEAR SYSTEMS WITH SINGULAR OR SEMIDEFINITE （1, 1） BLOCKS

An effective algorithm for solving large saddle-point linear systems, presented by Krukier et al., is applied to the constrained optimization problems. This method is a modification of skew-Hermitian triangular splitting iteration methods. We consider the saddle-point linear systems with singular or semidefinite （1, 1） blocks. Moreover, this method is applied to precondition the GMRES. Numerical results have confirmed the effectiveness of the method and showed that the new method can produce high-quality preconditioners for the Krylov subspace methods for solving large sparse saddle-point linear systems.     

ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.     

RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.     

保护私有信息的一般线性方程组计算协议

作为科学计算的一个重要问题,保护私有信息的线性方程组的求解在金融、机械及通信等领域有着广泛的应用.在不经意传输的意义下,利用有限域上计算Moore-Penrose伪逆矩阵的概率算法,设计新的安全协议,解决了隐私保护的一般线性方程组在有限域上的安全两方计算问题,并利用模拟范例证明该协议在半诚实模型下是安全的.     

GSOR方法最优迭代参数的简化推导

对于增广线性系统,Bai等研究了广义SOR方法（Bai Z Z,Parlett B,Wang Z Q.On generaliged successive overrelaxation methods for augmented linear systems.Numerische Mathematik,2005,102（1）：1-38）,并得到其最优迭代参数.给出了另外一种推导最优迭代参数的简化方法,这种方法对于求解其他参数加速定常迭代方法的最优迭代参数非常有意义.     

Necessary and sufficient conditions for distinguishability of linear control systems

Distinguishability plays a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of linear systems. However, the condition is not easy enough to verify. This paper will give a new equivalent condition which is relatively easy to verify.