离散Lyapunov矩阵方程X—AXB=C的一种数值解法

本文提供了求解离散Lyapunov矩阵方程的一种数值解法。首先讨论了系数矩阵为三对角形矩阵的公式解法,然后通过相似变换,将该方法推广到一般情形。     

Reduction of matrices by means of equivalent transformations and similarity transformations

The structure of polynomial matrices in connection with their reducibility by semiscalar-equivalent transformations and similarity transformations to simpler forms is considered. In particular, the canonical form of polynomial matrices without multiple characteristic roots with respect to the above transformations is indicated. This allows one to establish a canonical form with respect to similarity for a certain type of finite collections of numerical matrices. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 769–782, November, 1998.     

The Cauchy Problem for the System of Maxwell Equations

We consider the problem of analytic continuation of a solution to the system of Maxwell equations in a bounded spatial domain from data on part of the boundary of the domain. We construct an approximate solution to the problem using the Carleman matrix method.     

矩阵方程AX=B的转动不变解及其最佳逼近

利用矩阵的广义逆、奇异值分解、张量积和拉直算子,给出了矩阵方程AX=B有转动不变解的充分必要条件及有解时通解的表达式;给出了矩阵方程解集合中与给定矩阵的最佳逼近解的表达式.     

一种基于决策矩阵的DST-AHP多属性决策方法

针对层次分析法决策时存在两两判断、一致性检验次数过多和判断矩阵残缺性等问题,本文提出了一种基于决策矩阵的DST-AHP多属性决策方法。该方法结合决策矩阵的特征值,构建DST-AHP方法层次结构模型和判断矩阵,并根据判断矩阵定义不同属性下各焦元的基本概率分配函数;然后利用Dempster合成法则对基本概率分配函数值进行合成,依据合成后值对方案进行排序。最后对AHP和DST-AHP两种方法进行比较分析,说明该方法的有效性。     

关于复正定矩阵的判定

研究了复矩阵的正定性 ,给出了复正定矩阵的一系列判定条件 ,获得了一些新的结果 ,改进并推广了著名的 Hadam ard不等式、Fejer定理及郭忠的结果 ,削弱了华罗庚不等式的条件 .     

由主特征对构造对称三对角矩阵

本文讨论了由给定的两个特征对(λ1，x^(1))和(λ2，x^(2))来重构一个对称三对角矩阵的问题．给出了保证λ1为Tn的最大特征值的条件．     

A General Decomposition Algorithm for Parallel Queues with Correlated Arrivals

Queueing with correlated arrivals occurs when customers arrive at a set of queues simultaneously. The difficulty in analyzing systems with correlated arrivals is due to the fact that the individual queueing systems are stochastically dependent. Exact methods for analyzing these systems are computationally intensive and are limited to only a few special cases. In this paper, we consider a system of parallel queues with bulk service and correlated arrivals. We show how the matrix-geometric approach can be used to obtain the performance measures of the system. We also develop an algorithm for large systems that efficiently approximates the performance measures by decomposing it into individual queueing systems. Finally, we describe how the principles of our decomposition algorithm can be extended to analyze a variety of different parallel queueing systems with correlated arrivals. We then evaluate the accuracy of our algorithm through a numerical study.     

Robust output feedback stabilization for two-dimensional continuous systems in roesser form

This paper considers the problem of robust stabilization via dynamic output feedbackcontrollers for uncertain two-dimensional continuous systems described by the Roesser's state space model. The parameter uncertainties are assumed to be norm-bounded appearing in all the matrices of the system model. A sufficient condition for the existence of dynamic output feedback controllers guaranteeing the asymptotic stability of the closed-loop system for all admissible uncertainties is proposed. A desired dynamic output feedback controller can be constructed by solving a set of linear matrix inequalities. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the proposed method.