三对角对称矩阵逆特征问题存在唯一解的条件

n阶实对称矩阵称为n阶三对角对称矩阵,全体记为S0,若：i）b;＞0（i二1,2,…,l－1）称T为J。C0bi矩阵,全体记为SI;11）h＜0（d一1;又…,n－1）称T为负JacoN矩阵,全体记为h;iii）b;一叩一1,2,…,n－1）称T为不可约三对角对称矩阵,全体记为龙Jacobi矩阵的逆特征问题有广泛的应用;近年来有了较大发展［‘,’］．对由二个特征对构造相应的Jacobi矩阵或三对角对称矩阵问题的研究相对地比较成熟I’一义而对由三个特征对构造相应的Jacobi矩阵或三对角对称矩阵问题的研究却进展迟缓．文门对此作了一些尝试,本文具体研究：…     

五对角矩阵的特征值反问题

本文讨论了一类由五个特征值和相应特征向量构造实对称五对角矩阵的特征值反问题.研究了解的存在性以及存在解的充分必要条件,而且给出了算法和数值例子.     

Characterizing and approximating eigenvalue sets of symmetric interval matrices

We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries are perturbed, with perturbations belonging to some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner approximation algorithm, that in many case estimates exact bounds. To our knowledge, this is the first algorithm that is able to guarantee exactness. We illustrate our approach by several examples and numerical experiments.     

判定严格α-对角占优矩阵的充要条件

本文给出了几个判定严格α-对角占优矩阵的充要条件,进一步利用矩阵对角占优理论得到了判定非奇H-矩阵的一些充分条件,并用数值算例说明了这些结论的有效性．     

A symmetric preserving iterative method for generalized Sylvester equation

The generalized Sylvester matrix equation AX + YB = C is encountered in many systems and control applications, and also has several applications relating to the problem of image restoration, and the numerical solution of implicit ordinary differential equations. In this paper, we construct a symmetric preserving iterative method, basing on the classic Conjugate Gradient Least Squares (CGLS) method, for AX + YB = C with the unknown matrices X, Y having symmetric structures. With this method, for any arbitrary initial symmetric matrix pair, a desired solution can be obtained within finitely iterate steps. The unique optimal (least norm) solution can also be obtained by choosing a special kind of initial matrix. We also consider the matrix nearness problem. Some numerical results confirm the efficiency of these algorithms. It is more important that some numerical stability analysis on the matrix nearness problem is given combined with numerical examples, which is not given in the earlier papers. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Iterative refinement of computing inverse matrix

This work discusses the iterative refinement for finding the numerical inverse of a given non-singular matrix. The algorithm and convergence analysis of the iterative procedures are presented. Numerical examples are given to show the effectiveness of the iterative refinement.     

Dissipative control for linear systems by static output feedback

In this article, the problem of static output-feedback dissipative control is investigated for linear continuous-time system based on an augmented system approach. A necessary and sufficient condition for stability and strict (Q,S,R)-dissipativity of the closed-loop system is established in terms of a matrix inequality with free parametrisation matrix. An equivalent characterisation with some slack matrices for numerical solvability is then proposed. Based on this, a necessary and sufficient condition for the existence of a desired controller is given, and a corresponding iterative algorithm is developed to solve the condition. The effectiveness of results developed in this article is demonstrated by some numerical examples.     

A numerical approach for solving the high-order linear singular differential-difference equations

In this paper, a numerical method which produces an approximate polynomial solution is presented for solving the high-order linear singular differential-difference equations. With the aid of Bessel polynomials and collocation points, this method converts the singular differential-difference equations into the matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. This method gives the analytic solutions when the exact solutions are polynomials. Finally, some experiments and their numerical solutions are given; by comparing the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method. All of the numerical computations have been performed on a PC using some programs written in MATLAB v7.6.0 (R2008a).     

Jacobi矩阵逆特征问题存在唯一解的条件

（?）1.引 言设n阶Jacobi矩阵为记Jp,q为Jn的主子矩阵;即 关于Jacobi矩阵逆特征值问题的研究文献很多,类型有由两组谱数据或两个特征对（指特征值及相应的特征向量）构造Jacobi矩阵的元素[1].由主子阵及一组谱数据构造Jacobi     

Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays

In this paper, the problem of passivity analysis is investigated for uncertain stochastic fuzzy interval neural networks with time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. For the neural networks under study, a generalized activation function is considered, where the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By constructing proper Lyapunov-Krasovskii functional and employing a combination of the free-weighting matrix method and stochastic analysis technique, new delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs), which can be solved by some standard numerical packages. Finally, numerical examples are given to show the effectiveness and merits of the proposed method.