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1.
本文得到了正定Hermitian阵的Hadamard积的Schur补的一些不等式,进而,给出了他们的一些应用,这些改进了近期的一些结束. 相似文献
2.
Zhang Zhongzhi Liu ChangrongSchool of Math. Science Central South Univ. Changsha China Dept. of Math. Hunan City Univ. Yiyang China. Faculty of Mathematics Econometrics Hunan Univ. Changsha China. 《高校应用数学学报(英文版)》2004,(3)
§1 IntroductionWe considerthe following inverse eigenvalue problem offinding an n-by-n matrix A∈S such thatAxi =λixi,i =1,2 ,...,m,where S is a given set of n-by-n matrices,x1 ,...,xm(m≤n) are given n-vectors andλ1 ,...,λmare given constants.Let X=(x1 ,...,xm) ,Λ=(λ1 ,λ2 ,...,λm) ,then the above inverse eigenvalue problemcan be written as followsProblem Given X∈Cn×m,Λ=(λ1 ,...,λm) ,find A∈S such thatAX =XΛ,where S is a given matrix set.We also discuss the so-called opti… 相似文献
3.
张玉海 《高等学校计算数学学报》2001,23(1):73-78
1 引言及主要结果 本论文将要讨论如下问题[2,4]: 问题HG给定n+1个Hermite矩阵A=(aij)n×n和Ak=S和n个实数 ,求个实数c1,…,cn,使得A(c)= .的特征值为 对于上述问题,有解的充分条件已有许多研究结果,如[2,4,6].下面将利用Brouwer不动点定理给出新的充分条件. 本文的符号和定义如下: 对任意n阶Hermite矩阵B=(bij),记B(0)=B-diag(b11,b22,…,bnn),ρ(B)表示B的谱半径, {λ(B)}表示B的特征值(谱)集合,且设 表… 相似文献
4.
本文研究了Hermitian自反矩阵反问题的最小二乘解及其最佳逼近.利用矩阵的奇异值分解理论,获得了最小二乘解的表达式.同时对于最小二乘解的解集合,得到了最佳逼近解. 相似文献
5.
《高等学校计算数学学报(英文版)》2000,(Z1)
Main resultsTheorem 1 Let A be symmetric positive semidefinite.Let (?) be a diagonally compen-sated reduced matrix of A and Let (?)=σI+(?)(σ>0) be a modiffication(Stieltjes) matrixof (?).Let the splitting (?)=M-(?) be regular and M=F-G be weak regular,where M andF are symmetric positive definite matrices.Then the resulting two-stage method corre-sponding to the diagonally compensated reduced splitting A=M-N and inner splitting M=F-G is convergent for any number μ≥1 of inner iterations.Furthermore,the iteration 相似文献
6.
周知的正定矩阵A和B的Hadamard乘积矩阵不等式 :(A B) -1 ≤A-1 B-1 被精细为(A B) -1 ≤diag((A-1 (α) -1 B(α) ) -1 ,(A(α′) B-1 (α′) -1 ) -1 ) ,≤diag(A-1 (α) B(α) -1 ,A(α′) -1 B-1 (α′) )≤A-1 B-1 ,这里A(α)是A的主子矩阵且α′是α的补序列 ;同时给出了这些不等式的等式成立的充分必要条件 相似文献
7.
《高等学校计算数学学报(英文版)》2000,(Z1)
is gained by deleting the k~(th) row and the k~(th) column (k=1,2,...,n) from T_n.We put for-ward an inverse eigenvalue problem to be that:If we don’t know the matrix T_(1,n),but weknow all eigenvalues of matrix T_(1,k-1),all eigenvalues of matrix T_(k+1,k),and all eigenvaluesof matrix T_(1,n) could we construct the matrix T_(1,n).Let μ_1,μ_2,…,μ_(k-1),μ_k,μ_(k+1),…,μ_(n-1), 相似文献
8.
AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES 总被引:2,自引:0,他引:2
Haixia Liang Erxiong Jiang 《计算数学(英文版)》2007,25(5):620-630
In this paper, we discuss an inverse eigenvalue problem for constructing a 2n × 2n Jacobi matrix T such that its 2n eigenvalues are given distinct real values and its leading principal submatrix of order n is a given Jacobi matrix. A new sufficient and necessary condition for the solvability of the above problem is given in this paper. Furthermore, we present a new algorithm and give some numerical results. 相似文献
9.
AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES 总被引:7,自引:0,他引:7
Er-xiong Jiang 《计算数学(英文版)》2003,21(5):569-584
Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper. 相似文献
10.
反中心对称矩阵的广义特征值反问题 总被引:8,自引:0,他引:8
Given matrix X and diagonal matrix A , the anti-centrosymmetric solutions (A, B) and its optimal approximation of inverse generalized eigenvalue problem AX = BXA have been considered. The general form of such solutions is given and the expression of the optimal approximation solution to a given matrix is derived. The algorithm and one numerical example for solving optimal approximation solution are included. 相似文献
11.
THE SOLVABILITY CONDITIONS FOR INVERSE EIGENVALUE PROBLEM OF ANTI-BISYMMETRIC MATRICES 总被引:3,自引:0,他引:3
Dong-xiu Xie 《计算数学(英文版)》2002,(3)
AbstractThis paper is mainly concerned with solving the following two problems: Problem I. Given X Cnxm, A = diag( 1, 2, ..... , m) Cmxm . Find A ABSRnxn such thatAX = XAwhere ABSRnxn is the set of all real n x n anti-bisymmetric matrices. Problem II. Given A RnXn. Find A SE such thatwhere || || is Frobenius norm, and SE denotes the solution set of Problem I.The necessary and sufficient conditions for the solvability of Problem I have been studied. The general form of SB has been given. For Problem II the expression of the solution has been provided. 相似文献
12.
称为n阶Jacobi矩阵,振动反问题讨论由特征值(频率)和特征向量(模态)数据确定振动系统的物理参数,其研究对结构设计和结构物理参数识别具有重要意义,弹簧-质点系统的振动反问题归结为Jacobi矩阵的特征值反问题,这类问题已被许多学者研究[1-3]. 相似文献
13.
解非对称矩阵特征值问题的一种并行分治算法 总被引:3,自引:0,他引:3
1引言考虑矩阵特征值问题其中A是非对称矩阵.通过正交变换(如Householder变换或Givens变换),A可化为上Hessenberg形.因而,本文假设A为上Hessenberg矩阵,表示如下:不失一般性,进一步假设所有的(j=2,…,n),即认为A是不可约的关于如何求解上述问题,人们进行了不懈的努力,提出了许多行之有效的算法[1-8].其中分治算法因具有良好的并行性而引人注目.分治算法的典型代表是基于同伦连续的分治算法[2,3,4]和基于Newton迭代的分治算法[1].本文提出一种新的分… 相似文献
14.
We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefinite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those given in [1] for a simple cycle. We also derive some results for a partial Toeplitz PSD matrix specifying the Cnk pattern to have PSD completion and Toeplitz PSD completion. 相似文献
15.
APPROXIMATION ALGORITHM FOR MAX-BISECTION PROBLEM WITH THE POSITIVE SEMIDEFINITE RELAXATION 总被引:1,自引:0,他引:1
Da-chuan Xu Ji-ye Han 《计算数学(英文版)》2003,(3)
Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of crossing edges. In many interesting cases, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming. 相似文献
16.
实对称矩阵广义特征值反问题 总被引:10,自引:0,他引:10
戴华 《高校应用数学学报(A辑)》1992,7(2):167-176
本文研究如下实对称矩阵广义特征值反问题: 问题IGEP,给定X∈R~(n×m),1=diag(λ_II_k_I,…,λ_pI_k_p)∈R~(n×m),并且λ_I,…,λ_p互异,sum from i=1 to p(k_i=m,求K,M∈SR~(n×n),或K∈SR~(n×n),M∈SR_0~(n×m),或K,M∈SR_0~(n×n),或K∈SR~(n×n),M∈SR_+~(n×n),或K∈SR_0~(n×n),M∈SR_+~(n×n),或K,M∈SR_+~(n×m), (Ⅰ)使得 KX=MXA, (Ⅱ)使得 X~TMX=I_m,KX=MXA,其中SR~(n×n)={A∈R~(n×n)|A~T=A},SR_0~(n×n)={A∈SR~(n×n)|X~TAX≥0,X∈R~n},SR_+~(n×n)={A∈SR~(n×n)|X~TAX>0,X∈R~n,X≠0}. 利用矩阵X的奇异值分解和正交三角分解,我们给出了上述问题的解的表达式. 相似文献
17.
1引言在振动设计中,往往需要修改一个系统的数学模型的物理参数,这在数学上可以归结为矩阵的逆特征值问题或广义逆特征值问题(见[1]).例如,下面给出振动系统中刚度矩阵与质量矩阵的校正问题.设ω1,ω2,…,ωm(m≤n)是m个自然频率,φ1,φ2,…,φm是相应的振型,令Ω2=diag(ω12,ω22,…,ωm2),φ=(φ1,φ2,…,φm).设K为待校正的刚度矩阵,M为待校正的质量矩阵,它们满足下列条件(1.1)特征方程Kφ=MφΩ2, 相似文献
18.
对称正交对称矩阵逆特征值问题 总被引:27,自引:0,他引:27
Let P∈ Rn×n such that PT = P, P-1 = PT.A∈Rn×n is termed symmetric orthogonal symmetric matrix ifAT = A, (PA)T = PA.We denote the set of all n × n symmetric orthogonal symmetric matrices byThis paper discuss the following two problems:Problem I. Given X ∈ Rn×m, A = diag(λ1,λ 2, ... ,λ m). Find A SRnxnP such thatAX =XAProblem II. Given A ∈ Rnδn. Find A SE such thatwhere SE is the solution set of Problem I, ||·|| is the Frobenius norm. In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. The expression of the solution A* of Problem II is presented. We have proved that some results of Reference [3] are the special cases of this paper. 相似文献
19.
In this paper, by using the Guo-Krasnoselskii’s fixed-point theorem, we establish the existence and multiplicity of positive solutions for a fourth-order nonlinear eigenvalue problem. The corresponding examples are also included to demonstrate the results we obtained. 相似文献
20.
AnpingLiao ZhongzhiBai 《计算数学(英文版)》2003,21(2):175-182
Least-squares solution of AXB=D with respect to symmetric positive semidefinite matrix X is considered.By making use of the generalized singular value ecomposition,we derive general analytic formulas,and present necessary and sufficient conditions for guaranteeing the existence of the solution.By applying MATLAB 5.2,we give some numerical examples to show the feasibility and accuracy of this construciton technique in the finite precision arithmetic. 相似文献