AN ITERATED-SUBSPACE MINIMIZATION METHODS WITH SYMMETRIC RANK-ONE UPDATING

We consider an Iterated-Subspace Minimization(ISM) method for solving large-scale unconstrained minimization problems.At each major iteration of the method, a two-dimensional manifold, the iterated subspace, is constructed and an approximate minimizer of the objective function in this manifold then determined, and a symmetric rank-one updating is used to solve the inner minimization problem.     

对称正交矩阵反问题及其最佳逼近

本文主要讨论下面两个问题：问题Ⅰ：给定矩阵X,B∈R~(m×n),求对称正交矩阵A∈SOR~(m×m),使得AX=B．问题Ⅱ：给定矩阵(?)∈R~(m×m),求矩阵A~*∈S_E使得(?)这里S_E问题Ⅰ的解集合,‖·‖指Frobenius范数．本文首先讨论具有k阶对称主子阵的n(n＞k)阶正交矩阵的C-S分解,利用这个结果,得到了问题Ⅰ有解的充要条件和通解的一般形式．然后,对给定矩阵(?)∈R~(m×m),讨论了矩阵(?)在问题Ⅰ的解集合S_E中的最佳逼近,得到了最佳逼近解的表达式．     

对称自正交相似矩阵的逆特征值问题

1引言 对称自正交相似矩阵在结构力学及土木工程等中有实际应用,在许多实际问题中会遇到其逆特征值问题.因此研究此问题是有意义的.     

Jacobi矩阵逆特征问题解存在的条件

1 引言 对如下形状的n阶实对称三对角矩阵     

对称自正交相似矩阵逆特征值问题的推广

1引言对称自正交相似矩阵在结构力学、土木工程、数值分析等方面有实际应用,不少问题中常会遇到其逆特征值同题,研究它是有应用价值的．记(?)其中E=E_m(m阶单位阵)．容易验证1)T_k(E)·T_k(E)=E_(km)．2)T′_k(E)=T_k(E),其中T′_k(E)表示T_k(E)的转置．3) (?)其中k∈N(自然数)．令(?)当m=1时,T_k(E)就是k阶反序单位矩阵,即文[1]的(1)和(2)．定义1．1设A∈R~(2km×2km)满足SAS′=A,A′=A,则称A为对称自正交相似矩     

A NEW ALGORITHM FOR COMPUTING THE INVERSE AND GENERALIZED INVERSE OF THE SCALED FACTOR CIRCULANT MATRIX

A new algorithm for finding the inverse of a nonsingular scaled factor circulant matrix is presented by the Euclid＇s algorithm. Extension is made to compute the group inverse and the Moore-Penrose inverse of the singular scaled factor circulant matrix. Numerical examples are presented to demonstrate the implementation of the proposed algorithm.     

THE PERTURBATION THEORY FOR THE DRAZIN INVERSE AND ITS APPLICATIONS

Let A and E be an n×n matrices and B=A+E. Denote the Drazin inverse of A by AD In this paper, we give an upper bound for the relative error ||BD-AD||/||AD|| under certain circumstances. The error bound of the solution for singular equations Ax=b[Ind (A)=k,b∈R(Ak)] are also considered.     

弱群逆的扰动及其应用

<正>1引言设C_n,n表示n×n阶全体复矩阵的集合.记A^*,R(A),N(A),rk (A),‖A‖,ρ(A)分别表示矩阵A的共轭转置,值域,核空间,秩,谱范数,谱半径.记A的指标为Ind(A)=k,其中k是满足rk(A^k+1)=rk (A^k)成立的最小非负整数.进一步,     

张量积下核逆的扰动界

This paper introduces the Hartwig and Spindelb(o)ck decomposition for tensors and the definition of Tensor-core inverse.Then several properties and representations of Tensor-core inverse,are investigated.Further,we present some perturbation bounds for the Tensor-core inverse based on the T-product.     

关于带W权Drazin逆的表示定理及迭代方法

To study singular linear system, Cline and Greville[8] proposed the concept of W-weighted Drazin inverse for the rectangular matrices,where the properties were also discussed. The computation for the W-weighted Drazin inverse is of much interest, which is mainly divided into two kinds of methods: direct method[2,4,6] and iterative method[3,5,7,9,12,13]. In this paper, we study the iterative method and successive matrix squaring(SMS) method for the W-weighted Drazin inverse and generalize the main results in [12,13].     

A METHOD FOR SOLVING THE INVERSE SCATTERING PROBLEM FOR SHAPE AND IMPEDANCE

The inverse problem considered in this paper is to determine the shape and the impedance of an obstacle from a knowledge of the time-harmonic incident field and the phase and amplitude of the far field pattern of the scattered wave in two-dimension. Single-layer potential is used to approach the scattered waves. An approximation method is presented and the convergence of the proposed method is established. Numerical examples are given to show that this method is both accurate and easy to use.     

COMPUTING EIGENVECTORS OF NORMAL MATRICES WITH SIMPLE INVERSE ITERATION

It is well-known that if we have an approximate eigenvalue λ- of a normal matrix A of order n,a good approximation to the corresponding eigenvector u can be computed by one inverse iteration provided the position,say kmax,of the largest component of u is known.In this paper we give a detailed theoretical analysis to show relations between the eigenvecor u and vector xk,k=1,…,n,obtained by simple inverse iteration,i.e.,the solution to the system(A-λI)x=ek with ek the kth column of the identity matrix I.We prove that under some weak conditions,the index kmax is of some optimal properties related to the smallest residual and smallest approximation error to u in spectral norm and Frobenius norm.We also prove that the normalized absolute vector v=|u|/||u||∞ of u can be approximated by the normalized vector of (||x1||2,…||xn||2)^T,We also give some upper bounds of |u(k)| for those “optimal“ indexeds such as Fernando‘s heuristic for kmax without any assumptions,A stable double orthogonal factorization method and a simpler but may less stable approach are proposed for locating the largest component of u.     

微分连续正则化方法与一维声波方程系数反演问题求解

本文将求解非线性方程组的微分连续法与求解不问题的Ｔｉｋｈｏｎｏｖ正则化方法结合起来，形成了兼有大范围收性与稳定性的“微分连续正则化方法”，给出了方法的收敛性分析，文中最后给出的关于一维波动方程反问题的计算实例表明了方法的有效性。     

THE WAVE EQUATION APPROACH TO THE TWO-DIMENSIONAL INVERSE PROBLEM FOR A GENERAL BOUNDED DOMAIN WITH PIECEWISE SMOOTH MIXED BOUNDARY CONDITIONS

1 IntroductionLet fl be a simply connected bounded domain in R2 with a smooth boundary 0fl. Considerthe two-dimensional Robin problemwhere k denotes differentiation aIong the inward pointing normal to 0n and 7 is a positiv('constan. Denote its eigenvalues, counted according to multiplicity, byZayed alld Hassall[15'16] l1ave discussed the probleln (1. 1)-(1.2) fOr small / large impedance7 and have determned some geometric quantities of the don1ain n, using tl1e asymptotic ex-pansion of tlie s…     

一类二次特征值反问题的中心对称解及其最佳逼近

1引言给定n阶实矩阵M,C和K,二次特征值问题:求数λ和非零向量x使得Q(λ)x=0, (1．1)其中Q(λ)=λ2M λC K称为二次束．数λ和相应的非零向量x分别称为二次束Q(λ)的特征值和特征向量．Tisseur和Meerbergen概述了二次特征值问题的各种应用、数学理论和数值方法．在工程技术,特别是结构动力模型修正技术领域经常遇到与二次特征值问题相反的问题(称之为二次特征值反问题)．对阻尼结构进行动力分析时,应用有限元方法可得到系统的质量矩阵M,阻尼矩阵C和刚度矩阵K,从而可求得二次特征值问题的特征值(频率)和特征向量(振型)．但是有限元模型毕竟是实际结构系统的离散化,并且     

分块带状矩阵的逆

1引言如果分块矩阵A=(A_(ij))_(n×n)满足A_(ij)=O(j-i＞p且i-j＞q),其中A_(ij)为m阶矩阵,则称A为(p,q)-分块带状矩阵．分块带状矩阵在一些实际问题中经常出现,例如在量子场论中用途很广的非线性Schr(?)dinger方程的差分离散问题,解热传导问题等,都会遇到分块带状矩阵．常见的分块三对角矩阵,分块五对角矩阵都是特殊的分块带状矩阵．采用通常的方法求解分块带状矩阵的逆矩阵时,需要进行O(n~3)次m阶矩阵的运算．本文首先将分块带状矩阵扩充成可逆的分块上(下)三角矩阵,利用其逆矩阵导出了分块带状矩阵的逆矩阵表达式;进而利用所得到的公式分别推导了分块三对角矩阵及分块五对角矩阵的逆矩阵的快速算法,所需运算量为O(n~2)次m阶矩阵的运算．本文的结果扩充了文[1]等关于分块三对角阵求逆的相关结果．     

对称的运输问题及其逆问题

本文对［１,２,６］中提出的运输问题进行了推广,并提出了一个强多项式算法,从而改进了原有的结果．同时对对称的运输问题的逆问题进行了研究,并借助于最小费用循环流技术得到了一个强多项式算法．     

特殊矩阵反问题的最小二乘解及最佳逼近

1引言近年来,关于矩阵的反问题国内外有诸多学者都做了研究工作.如,双对称(反对称)矩阵反问题、中心对称(反中心对称)矩阵反问题、对称次反对称(反对称次对称)矩阵反问题.这些矩阵在信息论、线性系统理论及数值分析等领域中有其广泛应用.研究反问题的工具大多是奇异值分解(SVD)[6,8,9,5]、广义奇异值分解(GSVD)[4],且部分学者利用广义逆的方法[7]讨论上述的问题.本文的主要思想是找出这些矩阵的共同特点,利用矩     

态射的广义逆与等化子

本文以态射偶的等化子为工具研究态射的广义逆，对于态射f，给出了g为f^-,f^D和f^ 的充要条件，并在矩阵范畴中建立了齐次线性方程组解与等化子的关系。     

GLOBAL UNIQUENESS IN THE INVERSE ACOUSTIC SCATTERING PROBLEM WITHIN POLYGONAL OBSTACLES

§1. Introduction √ Let k ∈R, λ> 0 and i = ?1. We consider an acoustic scattering problem by animpenetrable obstacle D ? R2: ?u k2u = 0, in R2 \ D, …