带间断系数椭圆问题的P1非协调四边形元的加性 Schwarz 方法

本文讨论了带间断系数的二阶椭网问题的P1非协调四边形元的加性Schwarz方法.通过分析加性Schwaxz预处理后系统的特征值分布,我们证明了除少数小特征值外,其余所有特征值都有正的关于间断系数和网格尺寸拟一致的上下界.数值试验验证了我们的结论.     

用特征值刻画分式线性迭代数列的渐近性态

利用分式线性迭代数列系数矩阵的特征值,刻画这类数列的敛散性及收敛速度.     

平板几何迁移算子的特征值问题

研究L^p(1相似文献   

自适应间断Galerkin 有限元的多水平方法

本文讨论在自适应网格上间断Galerkin 有限元离散系统的局部多水平算法. 对于光滑系数和间断系数情形, 利用Schwarz 理论分析了算法的收敛性. 理论和数值试验均说明算法的收敛率与网格层数以及网格尺寸无关. 对强间断系数情形算法是拟最优的, 即收敛率仅与网格层数有关.     

基于Crouzeix-Raviart元的界面浸入有限元方法及其收敛性分析

本文对具间断系数的二阶椭圆界面问题提出一种浸入有限元方法(theimmersed finite element method), 即在界面单元上采用依赖于界面的线性多项式空间离散, 而在非界面单元上采用Crouzeix-Raviart非协调元离散. 论证表明, 该方法具有对界面问题解的最优L²-模和H¹-模收敛精度.     

变系数部分线性测量误差模型的B-样条估计（英文）

本文研究变系数部分线性测量误差模型的估计问题.利用纠偏方法,获得参数分量修正的最小二乘估计和非参数分量的B-样条估计.证明参数估计是相合的,渐近正态的;系数函数的B-样条估计达到非参数回归估计的最优收敛速度.模拟结果表明该方法是有效的.     

变系数模型的小波估计

变系数模型是近年来文献中经常出现的一种统计模型.本文主要研究了变系数模型的估计问题,提出运用小波的方法估计变系数模型中的系数函数,小波估计的优点是避免了象核估计、光滑样条等传统的变系数模型估计方法对系数函数光滑性的一些严格限制. 并且,我们还得到了小波估计的收敛速度和渐近正态性.模拟研究表明变系数模型的小波估计有很好的估计效果.     

非协调元特征值渐近下界

利用有限元收敛速度下界的结果获得某些非协调元方法新的Aubin-Nitsche估计形式,然后再结合非协调元特征值的展开式获得不需要额外条件下非协调元特征值渐近下界的结果.     

几乎各向同性的高维空间分数阶扩散方程的分块快速正则Hermite分裂预处理方法

一类空间分数阶扩散方程经过有限差分离散后所得到的离散线性方程组的系数矩阵是两个对角矩阵与Toeplitz型矩阵的乘积之和.在本文中,对于几乎各向同性的二维或三维空间分数阶扩散方程的离散线性方程组,采用预处理Krylov子空间迭代方法,我们利用其系数矩阵的特殊结构和具体性质构造了一类分块快速正则Hermite分裂预处理子.通过理论分析,我们证明了所对应的预处理矩阵的特征值大部分都聚集于1的附近.数值实验也表明,这类分块快速正则Hermite分裂预处理子可以明显地加快广义极小残量(GMRES)方法和稳定化的双共轭梯度(BiCGSTAB)方法等Krylov子空间迭代方法的收敛速度.     

自共轭全连续算子谱逼近的保序收敛性

讨论自共轭全连续算子T谱逼近的保序收敛性质. 在近似算子T_h依范数收敛于T的条件下证明了T_h$的第k个特征值收敛于T的第k个特征值(对正特征值按从大到小顺序排列, 对负特征值按从小到大顺序排列, 并按其重数重复计数). 并把这结果用于自共轭椭圆微分算子特征值问题协调有限元法、非协调有限元法与混合有限元法, 证明了用这些方法求得的第k个近似特征值都收敛于第k个准确特征值.     

非线性特征值问题的二次近似方法

本文研究求解非线性特征值问题的数值方法.基于矩阵值函数的二次近似,将非线性特征值问题转化为二次特征值问题,提出了求解非线性特征值问题的逐次二次近似方法,分析了该方法的收敛性.结合求解二次特征值问题的Arnoldi方法和Jacobi-Davidson方法,给出求解非线性特征值问题的一些二次近似方法.数值结果表明本文所给算法是有效的.     

A spectral projection method for transmission eigenvalues

We consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides whether the region contains eigenvalue(s) or not. It is particularly suitable to test whether zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples.     

Guaranteed lower eigenvalue bounds for the biharmonic equation

The computation of lower eigenvalue bounds for the biharmonic operator in the buckling of plates is vital for the safety assessment in structural mechanics and highly on demand for the separation of eigenvalues for the plate’s vibrations. This paper shows that the eigenvalue provided by the nonconforming Morley finite element analysis, which is perhaps a lower eigenvalue bound for the biharmonic eigenvalue in the asymptotic sense, is not always a lower bound. A fully-explicit error analysis of the Morley interpolation operator with all the multiplicative constants enables a computable guaranteed lower eigenvalue bound. This paper provides numerical computations of those lower eigenvalue bounds and studies applications for the vibration and the stability of a biharmonic plate with different lower-order terms.     

On the quadratic two-parameter eigenvalue problem and its linearization

We introduce the quadratic two-parameter eigenvalue problem and linearize it as a singular two-parameter eigenvalue problem. This, together with an example from model updating, shows the need for numerical methods for singular two-parameter eigenvalue problems and for a better understanding of such problems.There are various numerical methods for two-parameter eigenvalue problems, but only few for nonsingular ones. We present a method that can be applied to singular two-parameter eigenvalue problems including the linearization of the quadratic two-parameter eigenvalue problem. It is based on the staircase algorithm for the extraction of the common regular part of two singular matrix pencils.     

Inverse unitary eigenproblems and related orthogonal functions

Summary. This paper explores the relationship between certain inverse unitary eigenvalue problems and orthogonal functions. In particular, the inverse eigenvalue problems for unitary Hessenberg matrices and for Schur parameter pencils are considered. The Szeg? recursion is known to be identical to the Arnoldi process and can be seen as an algorithm for solving an inverse unitary Hessenberg eigenvalue problem. Reformulation of this inverse unitary Hessenberg eigenvalue problem yields an inverse eigenvalue problem for Schur parameter pencils. It is shown that solving this inverse eigenvalue problem is equivalent to computing Laurent polynomials orthogonal on the unit circle. Efficient and reliable algorithms for solving the inverse unitary eigenvalue problems are given which require only O() arithmetic operations as compared with O() operations needed for algorithms that ignore the structure of the problem. Received April 3, 1995 / Revised version received August 29, 1996     

Asymptotics of eigenvalues of the nonlinear eigenvalue problem arising from the near mixed-mode crack-tip stress-strain field problems

In the present paper, approximate analytical and numerical solutions to nonlinear eigenvalue problems arising in nonlinear fracture mechanics in studying stress-strain fields near a crack tip under mixed-mode loading are presented. Asymptotic solutions are obtained by the perturbation method (the artificial small parameter method). The artificial small parameter is the difference between the eigenvalue corresponding to the nonlinear eigenvalue problem and the eigenvalue related to the linear “undisturbed” problem. It is shown that the perturbation technique is an effective method of solving nonlinear eigenvalue problems in nonlinear fracture mechanics. A comparison of numerical and asymptotic results for different values of the mixity parameter and hardening exponent shows good agreement. Thus, the perturbation theory technique for studying nonlinear eigenvalue problems is offered and applied to eigenvalue problems arising in fracture mechanics analysis in the case of mixed-mode loading.     

On linearizations of the quadratic two-parameter eigenvalue problem

We present several transformations that can be used to solve the quadratic two-parameter eigenvalue problem (QMEP), by formulating an associated linear multiparameter eigenvalue problem. Two of these transformations are generalizations of the well-known linearization of the quadratic eigenvalue problem and linearize the QMEP as a singular two-parameter eigenvalue problem. The third replaces all nonlinear terms by new variables and adds new equations for their relations. The QMEP is thus transformed into a nonsingular five-parameter eigenvalue problem. The advantage of these transformations is that they enable one to solve the QMEP using existing numerical methods for multiparameter eigenvalue problems. We also consider several special cases of the QMEP, where some matrix coefficients are zero     

Calculating the minimal/maximal eigenvalue of symmetric parameterized matrices using projection

In applications of linear algebra including nuclear physics and structural dynamics, there is a need to deal with uncertainty in the matrices. We focus on matrices that depend on a set of parameters ω and we are interested in the minimal eigenvalue of a matrix pencil ( A , B ) with A , B symmetric and B positive definite. If ω can be interpreted as the realization of random variables, one may be interested in statistical moments of the minimal eigenvalue. In order to obtain statistical moments, we need a fast evaluation of the eigenvalue as a function of ω . Because this is costly for large matrices, we are looking for a small parameterized eigenvalue problem whose minimal eigenvalue makes a small error with the minimal eigenvalue of the large eigenvalue problem. The advantage, in comparison with a global polynomial approximation (on which, e.g., the polynomial chaos approximation relies), is that we do not suffer from the possible nonsmoothness of the minimal eigenvalue. The small‐scale eigenvalue problem is obtained by projection of the large‐scale problem. Our main contribution is that, for constructing the subspace, we use multiple eigenvectors and derivatives of eigenvectors. We provide theoretical results and document numerical experiments regarding the beneficial effect of adding multiple eigenvectors and derivatives.     

复Monge－Ampere方程的特征值问题

讨论了复空间中强拟凸域上的复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的特征值问题，证明了特征值问题解的存在唯一性，并给出了这个特征值与一类复空间中复Ｌａｐｌａｃｅ算子的第一特征值的关系，最后利用特征值及特征函数的存在性讨论了一类复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的解的存在性及其分歧．     

Eigenvalue immobility measures for Markov chains 1

Two eigenvalue measures of immobility are proposed for social processes described by a Markov chain. One is the second largest eigenvalue modulus of the chain's transition matrix. The other is the second largest eigenvalue modulus of a closely related transition matrix. The two eigenvalue measures are compared to each other and to correlation and regression‐to‐the‐mean measures. In illustrative applications to intergenerational occupational mobility, the eigenvectors corresponding to the eigenvalue measures are found to be good proxies for occupational status rankings for a number of countries, thus reinforcing a pattern noted by Klatsky and Hodge and by Duncan‐Jones.