正规矩阵的任意扰动

设A为n×n矩阵,其特征值为λ1,λ2,…,λn;矩阵B=A+X之特征值为μ1,μ2,…,μn.若A,B均为正规矩阵,由Wielandt-Hoffman定理[1],存在1,2,…,n的一个排列k1,k2,…,kn,使得nj=1|λj-μkj|2≤‖X‖2F,(1)其中‖·‖F表示Frobenius范数.又,在同样条件下,存在1,2,…,n的一个排列l1,l2,…,ln,使得对1≤j≤n均有|λj-μlj|≤2.91‖X‖2,(2)其中‖·‖2表示谱范数,这是R.Bhatia等人的结果[2].本文旨在讨论A为正规矩阵,B为任意矩阵时特征值的扰动估计,得到了几个扰动定理,分别推广了上述两个结果.本文用CH表示矩阵C的共轭转置,trC表示C的迹;…     

广义延拓矩阵在乘法扰动下特征空间的相对扰动界

在矩阵A与其扰动矩阵A有相同分块的谱分解下,对于以A为母矩阵的广义延拓矩阵凡（A）及以A为母矩阵的广义延拓矩阵凡（A）,使用特征值双分离度方法,给出了广义延拓矩阵n（A）与其扰动矩阵n（A）的特征空间在乘法扰动下的相对扰动界．     

关于正规矩阵对广义特征值新的扰动界限

本文考虑了正规矩阵对的任意扰动时广义特征值的变化情况,给出了正规矩阵对任意扰动的Hoffman-Wielandt型扰动界,推广了正规矩阵对的相应的扰动结果.     

不变子空间上特征值的扰动

1引言设矩阵A∈C~(n×n),B∈C~(m×m),Q∈C~(n×m)为列满秩矩阵,令R=AQ-QB．当R的范数很小的时候,我们分析矩阵B的特征值对A的特征值的逼近性．当A,B都是Hermite阵时,上述问题已经被Kahan解决．近年来,对可对角化矩阵的情形,取得了一些新的成果．[4][5][6]中给出了几个范数不等式,并应用于矩阵特征值     

Sylvester方程在矩阵扰动分析中的应用

§1.引言 矩阵扰动分析的研究对于矩阵论的发展及数值分析问题计算结果的分析和处理都有重要意义.有关特征值、广义特征值及最小二乘问题的主要研究结果均含于[1]中,[5]运用二次方程根的判别法通过对代数Ricatti方程的解的估计给出了QR分解因子及Cholesky因子的扰动分析,但论证方法及所得结果都比较复杂且所求条件很强.[3]和     

代数特征值反问题之解的稳定性分析

考虑如下代数特征值反问题: 问题 G(A;{A_k}_1~n;λ).设 A=(a_(ij)),A_k=(a_(ij)~((k))),k=1,…,n是n+1个n×n的实对称矩阵,λ=(λ_1,…,λ_n)是n维实向量且λ_i≠λ_j,i≠j.求n维实向量c=(c_1,…,c_n)~T,使矩阵A(c)=A+sum from k=1 to n (c_kA_k)的特征值是λ_1,…,λ_n. 这一问题是经典加法问题的推广.当A_k-e_ke_k~~T(e_k是n阶单位阵的第k列)时,     

正则矩阵对的广义特征值扰动定理

1.引言 关于普通特征值扰动的Bauer-Fike定理已被推广到A为非可对角化的情形.与此相应,广义特征值的扰动问题,亦有类似的结论.将[1]中的结论稍加改进并且推广至一般正则对的情形,是本文一部分内容,另一部分是研究广义近似特征值以及广义近似不变子空间的特征值扰动,本文采用的范数不局限于谱范数,而是一般的p-范数(1≤p≤+∞).     

广义特征值的扰动界限(Ⅰ)

到目前为止,关于广义特征值的扰动,已经建立了一些界限估计,但一般正则对的扰动界限难以算出.首先,定义某些基本参数,并利用这些参数建立几个关于一般正则矩阵对的广义特征值的扰动定理.这些定理给出的扰动界限的上界估计,一般是可以算出的.     

一般矩阵元素振动秩的一个定理

在文[1]列满矩阵元素扰动秩的稳定性基础上,运用矩阵的范数,分析,研究一般矩阵A∈C^m&;#215;n元素扰动秩的问题,得出“存在ε＞0,只要δA∈C^m&;#215;n,满足||δ||＜ε,则有A＋δA∈U^nk=rC^m&;#215;nk=r的结论。     

一类矩阵特征值的扰动

本文讨论可正规化矩阵和可对称化矩阵特征值的扰动。所谓可正规化矩阵和可对称化矩阵分别指相似于正规矩阵和Hermite矩阵的矩阵。     

SR分解的乘法扰动界

In this paper, we present the first order perturbation bounds for the SR factorization with respect to left multiplicative perturbation, and the first order and rigorous perturbation bounds for this factorization with respect to right multiplicative perturbation.Moreover, taking the properties of SR factors into consideration, we also provide some refined perturbation bounds.     

Linearized perturbation method for stochastic analysis of a rill erosion model

The linearization and correction method (LCM) proposed by He is a simple and effective perturbation technique to solve nonlinear equations. To analyze the random properties of rill erosion model, a new stochastic perturbation technique called linearized perturbation method is developed by combining the traditional stochastic perturbation method with the LCM. Comparisons between the numerical results obtained by the linearized perturbation method and those obtained by Monte Carlo method indicated an excellent agreement. However, the calculation efficiency of the linearized perturbation method is higher.     

Perturbation Sensitivity and Limit Loads of Shells

The perturbation sensitivity and its influence on the limit loads of shells are widely discussed phenomena. Both phenomena may be classified with respect to the type of perturbation. As perturbations influence the stability of shells, the identification of unfavourable perturbations is essential. The perturbation energy concept enables to identify unfavourable non–initial perturbation loads and to evaluate the perturbation sensitivity of fundamental states by the perturbation energy. This measure is also the basis for a load–level–specific optimisation of the perturbation sensitivity. Hence, the present paper discusses primarily the perturbation sensitivity of axially loaded cylindrical shells with different boundary conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于钱氏摄动法的高阶解的计算机求解和收敛性的研究

本文借助于中心受集中载荷圆板小挠度问题的积分方程,获得了摄动参数为中心挠度的任意n阶摄动解的解析式.于是,任意次摄动解的所有待定系数能用计算机求解.因此,获得了相当高阶的摄动解.在此基础上,讨论了钱氏摄动法的渐近性和适用区.     

Influence diagnostics for the proportional hazards model

Influence diagnostics based on Cook's curvature diagnostic (1986) are developed for the proportional hazards model. Three perturbation schemes are considered: perturbation of the likelihood, perturbation of the censoring information and perturbation of covariate values.     

On the perturbation of the Q‐factor of the QR factorization

This paper gives normwise and componentwise perturbation analyses for the Q‐factor of the QR factorization of the matrix A with full column rank when A suffers from an additive perturbation. Rigorous perturbation bounds are derived on the projections of the perturbation of the Q‐factor in the range of A and its orthogonal complement. These bounds overcome a serious shortcoming of the first‐order perturbation bounds in the literature and can be used safely. From these bounds, identical or equivalent first‐order perturbation bounds in the literature can easily be derived. When A is square and nonsingular, tighter and simpler rigorous perturbation bounds on the perturbation of the Q‐factor are presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Some New Perturbation Bounds for the Generalized Polar Decomposition

The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented.     

Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces

In this paper, we study the perturbation problem for oblique projection generalized inverses of closed linear operators in Banach spaces. By the method of the perturbation analysis of linear operators, we obtain an explicit perturbation theorem and error estimates for the oblique projection generalized inverse of closed linear operators under the T-bounded perturbation, which extend the known results on the perturbation of the oblique projection generalized inverse of bounded linear operators in Banach spaces.     

Solutions of evolution inclusions generated by a difference of subdifferentials

An evolution inclusion with the right-hand side containing the difference of subdifferentials of proper convex lower semicontinuous functions and a multivalued perturbation whose values are nonconvex closed sets is considered in a separable Hilbert space. In addition to the original inclusion, we consider an inclusion with convexified perturbation and a perturbation whose values are extremal points of the convexified perturbation that also belong to the values of the original perturbation. Questions of the existence of solutions under various perturbations are studied and relations between solutions are established. The primary focus is on the weakening of assumptions on the perturbation as compared to the known assumptions under which existence and relaxation theorems are valid. All our assumptions, in contrast to the known assumptions, concern the convexified rather than original perturbation.     

Euler-Bernoulli梁的高阶二次摄动解及收敛性讨论

首次用解析的方式给出了Euler-Bernoulli梁后屈曲与非线性弯曲问题的高阶二次摄动解答.假定梁的中线不可伸长，用精确曲率公式与能量变分原理导出了非线性Euler-Bernoulli梁的模型.通过与精确解或高阶摄动解的比较，讨论了二次摄动解答的收敛性及适用域.得到主要结论如下:低阶摄动解适用于描述梁的初始后屈曲阶段及初始非线性弯曲阶段；更高阶次的摄动解适用于描述梁的深度后屈曲以及深度非线性弯曲.从这个意义上去说，该文不仅仅指出某些文献上的部分结果不精确是由于摄动解答超出了其特定的适用域，并且还进一步发展与完善了二次摄动法.