求实对称矩阵特征向量与特征值的新方法

为了避免现有特征向量与特征值求解方法的复杂运算,本文给出了两种新解法——最优化法与自组织网络法。它们都采用参数随机逼近策略,便于并行计算或网络实现,最后经实验证明了新法的有效性。     

Eigenvalues of Set-Valued Operators in Banach Spaces

This work deals with the spectral analysis of set-valued operators from a Banach space X into its dual space X^*. The main goal of the paper is to study semicontinuity properties of the spectrum operator.Mathematics Subject Classifications (2000) 47H04, 47H12, 58C40.UMR 2071 Universidad de Chile-CNRS.     

一种分数余弦变换及应用

定义了一种分数余弦变换的形式，用前两个整数阶余弦变换的线性叠加构造分数余弦变换。然后基于特征值及特征向量计算的方法将其扩展成K周期形式，推导了两种计算分数余弦变换的算法，并且讨论了与Pei定义的分数余弦变换之间的关系。最后探讨了其在音频信号数字水印中的应用。     

对一般算符是否存在共同本征态问题的讨论

对任意算符不确定关系的一般表述加以定义,从而给出判断任意算符存在共同本征态的必要条件,并将其应用于非厄米算符的情形.     

非线性特征方程的重根特征灵敏度

在大型结构工程的控制工程中，对非线性特征方程的需求将愈来愈多，在以非线性特征方程分析结构或控制系统的动态特性，进而指导系统的动态设计时，其特征灵敏度是不可缺少的信息。为此，本文针对具有生根的非线性特征方程的特征导数计算提出了一种较为实用的方法。     

椭圆PDE-约束优化问题的一个预条件子

针对由Galerkin有限元离散椭圆PDE-约束优化问题产生的具有特殊结构的3×3块线性鞍点系统,提出了一个预条件子并给出了预处理矩阵特征值及特征向量的具体表达形式.数值结果表明了该预条件子能够有效地加速Krylov子空间方法的收敛速率,同时也验证了理论结果.     

On Existence of Common Fixed Points Under Lipschitz-Type Mapping Pairs with Applications

In this paper, we propose some su?cient conditions to obtain the existence of common fixed points for a pair of self-mappings satisfying Lipschitz-type conditions in noncomplete metric space. Our results improve and extend the results of Pant [Common fixed points of Lipschitz-type mapping pairs, J. Math. Anal. Appl. 240, (1999), 280–283] and Khan et al. [Coincidences of Lipschitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9–10), (2007), 1165–1177]. As an application of our results we solve an eigenvalue problem for operators defined on a normed space.     

特征向量导数计算的Lanczos方法

本文对特征向量导数计算的Ｌａｎｃｚｏｓ法进行了改进，指出Ｌａｎｃｚｏｓ法对方程的缩阶效率取决于初始向量的选择，介绍了Ｌａｎｃｚｏｓ方法的发展，提出采用频率移位法选择初始Ｌａｎｃｚｏｓ向量。通过理论分析及计算机仿真说明移位Ｌａｎｃｚｏｓ方法可以将较大的方程组缩为一阶方程，在计算精度与效率上大大优于任选向量Ｌａｎｃｚｏｓ法和迭代Ｌａｎｃ－ｚｏｓ法     

Some applications of Banach algebra techniques

We consider some functional Banach algebras with multiplications as the usual convolution product * and the so‐called Duhamel product ?. We study the structure of generators of the Banach algebras (C⁽ⁿ⁾[0, 1], *) and (C⁽ⁿ⁾[0, 1], ?). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space L^p[0, 1] by the formula (C_φf)(x) = f(φ(x)).     

Approximate method for eigensensitivity analysis of a defective matrix

Based on the exact modal expansion method, an arbitrary high-order approximate method is developed for calculating the second-order eigenvalue derivatives and the first-order eigenvector derivatives of a defective matrix. The numerical example shows the validity of the method. If the different eigenvalues μ(1),…,μ(q) of the matrix are arranged so that |μ(1)|≤?≤|μ(q)| and satisfy the condition that |μ(q₁)|<|μ(q₁+1)| for some q₁<q, and if the approximate method only uses the left and right principal eigenvectors associated with μ(1),…,μ(q₁), then associated with μ(h)(h≤q₁) the errors of the eigenvalue and eigenvector derivatives by the pth-order approximate method are nearly proportional to |μ(h)/μ(q₁+1)|^p+1.