求解对称三对角矩阵特征值的一种新的分而治之算法

1．引言关于对称三对角矩阵特征值问题，已有许多行之有效的算法，如QR算法、二（）分法和Jacobi迭代法等．本文构造一种适于并行处理的新算法——分而治之算法．设人是nX。阶的对称三对角实矩阵，形式如下：不失一般性，设所有的b；／0（i＝1，2，…，n—1），即认为A是不可约的．不同于CuPPen’s方法l‘］，我们将A划分如下：其中Al，AZ分别是kXk和（n—k）X（。一k）的实对称H对角矩阵·AI，AZ也可以递归地作类似的划分．分而治之算法的基本思想就是把原问题划分成若干个子问题，从子问题的解出发求解原问题．这是一个递归过程，…     

解实对称矩阵特征值问题的并行算法

51．二分／多分法二分／多分法（BS／MS）是当前最常用的解实对称矩阵特征值问题的并行算法．这个算法也可解Hermitian矩阵的特征值问题、实对称矩阵和Hermitain矩阵的广义特征值问题，更适用于解实对称三对角线矩阵特征值问题．丑．1实对称三对角经矩阵特征值问题假设实对称三对角线矩阵T为T的A矩阵T－Al的各级前生子式p朴），i二01，2，…，。可用三项递推公式产生其中见由一det（T－Al）．序列只（A），i一01，…，n具有Sturm序列性质；即序列的相邻项符号不同数等于T的小于人的特征值个数．在实际计算时，因为只（A）容易上、下…     

对称Toeplitz矩阵相乘的快速算法

§1．引言在数字信号处理的领域中，经常会遇到一种特殊形状的ToePlitz矩阵它除了具有一般T型矩阵的特点（主对角线上的各元素彼此相等，平行于主对角线上的元素也彼此相等，矩阵中的元素关于次对角线对称）外，还是一个对称矩阵，即形如（1）的矩阵是对称T型矩阵·因它可由矩阵第一行的元素唯一确定，故可简记为ST（ti，tZ，…，in）ESTM．关于对称T型系统的快速算法，已有不少研究成果，如求逆的Thench算法，解线性方程组的Levinson算法等l’，‘，’］．本文研究两个n阶对称T型矩阵相乘的快速算法．两个n阶对称T型矩阵的乘积，一…     

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     

由两个特征对构造正定Jacobi矩阵

132 数值计算与计算机应用2002 it巨1.引言具有如下形状的实对称矩阵:ldl hi \Ibid。。6,l人=I”.”·.’·.I 门)16、_,tL、_fo、_11\ b、;_IG、l称为n阶实对称三对角矩阵.若人还满足:(a)b;>     

解实对称矩阵特征值并行快速Jacobi方法

<正> 本文对传统的Jacobi 变换进行变形,且在此基础上设计了快速方法。对一次扫描而言,进行变形可省2·(((n(n-1))/2)-2[(n+1)/2]+1)次矩阵乘法([x]表示≤x 的最大整数),快速方法对固定j 而言,省了一次开平方计算。一、Jacobi 变换变形对n 阶实对称矩阵A=[a_(ij)=[(?)]i,j=1,2,…n,鉴于A 的对称性,仅考虑i相似文献   

由谱数据数值稳定地构造Jacobi矩阵

所谓Jacobi矩阵是指如下形式的矩阵:并且b_i>0(i=1,…,n-1)。 我们用J_(n-1)表示J_n的n-1阶顺序主子矩阵。 1967年,Hochstadt提出了如下Jacobi矩阵特征值反问题。 问题1。给定两组实数{λ}_(i=1)~n和{μ_i}_(i=1)~(n-1)且满足     

奇数元二阶相关免疫对称布尔函数的构造

n元m阶相关免疫对称函数的构造等价于方程[i=0n-2Cin-2xi=i=0n-2Cin-2xi+1]在二元域上的求解。通过对该方程及其等价方程解的关系讨论,给出了构造奇数元二阶相关免疫对称函数的算法。     

一类可对称化矩阵反问题的最小二乘解

1.引言 用Rn×m,ORn×n,SRn×n及ASRn×n分别表示n×m实矩阵,n阶实正交矩阵,n阶实对称矩阵和n阶实反对称矩阵的全体组成的集合.用S⊥表示集合S的正交补,A(?)B表示A和B的正交直和.设A,B∈Rn×m,定义A与B的内积为     

解一阶线性常微分方程组一般边值问题的线性最小二乘法

设有一阶线性常微分方程组边值问题 y_i＇(x)=sum from i=1 to n [a_(ij)(x)y_i(x)+f_i(x)]0相似文献   

三对角对称矩阵逆特征问题

In this paper, four inverse eigenproblems with giventhree eigenvalues and corresponding eigenvectors are considered, somenecessary and sufficient conditions under which there exists a uniquesolution for these problems are given. Furthermore some numerical algorithmsand some numerical experiments are given.     

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．     

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.     

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     

On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty

This paper investigates the robust stability of uncertain linear neutral systems with time-varying discrete delay. A delay-dependent stability criterion is obtained and formulated in the form of a linear matrix inequality. Two numerical examples are given to indicate significant improvements over some existing results.     

一类不确定中立型系统的时滞相关稳定准则

本文讨论了一类定常系数时变时滞中立型系统的时滞相关稳定性. 以线性矩阵不等式形式给出了新的时滞相关渐近稳定标准. 二个数值例子表明本文结果比先前结论有较小的保守性.     

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.     

Numerical solution of linear Fredholm integral equations system by rationalized Haar functions method

In this paper rationalized Haar functions are developed to approximate the solutions of the linear Fredholm integral equations system. Properties of rationalized Haar functions are first presented, the operational matrix of the product of rationalized Haar functions vector is utilized to reduce the computation of Fredholm integral equations system to some algebraic equations. Finally, numerical result are given which support the theoretical results.