三对角对称矩阵的逆特征问题

三对角对称矩阵的逆特征问题胡锡炎，周小庄（湖南大学）ＩＮＶＥＲＳＥＥＩＧＥＮＰＲＯＢＬＥＭＳＦＯＲＴＲＩＤＩＡＧＯＮＡＬＳＹＭＭＥＴＲＩＣＭＡＴＲＩＣＥＳ￥ＨｕＸｉｙａｎ；ＺｈｏｕＸｉａｏｚｈｕａｎｇ（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ...     

三对角对称矩阵逆特征问题存在唯一解的条件

n阶实对称矩阵称为n阶三对角对称矩阵,全体记为S0,若：i）b;＞0（i二1,2,…,l－1）称T为J。C0bi矩阵,全体记为SI;11）h＜0（d一1;又…,n－1）称T为负JacoN矩阵,全体记为h;iii）b;一叩一1,2,…,n－1）称T为不可约三对角对称矩阵,全体记为龙Jacobi矩阵的逆特征问题有广泛的应用;近年来有了较大发展［‘,’］．对由二个特征对构造相应的Jacobi矩阵或三对角对称矩阵问题的研究相对地比较成熟I’一义而对由三个特征对构造相应的Jacobi矩阵或三对角对称矩阵问题的研究却进展迟缓．文门对此作了一些尝试,本文具体研究：…     

求分块周期三对角矩阵逆矩阵的新算法

根据分块三对角矩阵逆矩阵的特殊结构,利用其LU和UL分解,并使用Sheman-Morrison-Woodbury公式,得到一个求分块周期三对角矩阵逆矩阵的新算法,并由该算法得到求周期三对角矩阵和对称周期三对角矩阵逆矩阵的新算法。新算法比传统算法的计算复杂度和计算时间要低。     

对称箭形矩阵最大最小特征对的逆特征值问题的一个有效算法

研究一个对称箭形矩阵的逆特征值问题：给定非零向量x∈R^n,y∈R^k,k≤n,以及两个实数λ〉μ,求对称箭形矩阵A,使得（λ,x）是对称箭形矩阵A的最大特征对,而（μ,y）是A的k阶顺序主子阵Ak的最小特征对。给出该问题有解的充分必要条件,并且给出一个算法计算该问题的一个解,数值实例说明是可行的。     

基于分治法求解对称三对角矩阵特征问题的混合并行实现

基于对称三对角矩阵特征求解的分而治之方法,提出了一种改进的使用MPI/Cilk模型求解的混合并行实现,结合节点间数据并行和节点内多任务并行,实现了对分治算法中分治阶段和合并阶段的多任务划分和动态调度.节点内利用Cilk任务并行模型解决了线程级并行的数据依赖和饥饿等待等问题,提高了并行性;节点间通过改进合并过程中的通信流程,使组内进程间只进行互补的数据交换,降低了通信开销.数值实验体现了该混合并行算法在计算效率和扩展性方面的优势.     

行对称矩阵广义逆的快速求解公式

对行对称矩阵的QR分解进行了研究,在此基础上给出了求行对称矩阵广义逆的快速求解公式,并给出了证明。将QR分解方法应用于该类行对称矩阵的广义逆的求解过程,既利用了QR分解保证足够的精度,又可大大降低求解一类具有该结构矩阵的广义逆的计算量和存储量。     

一类块三对角矩阵的计算

通过构造一个矩阵序列,给出了一类块三对角线性方程组的解耦算法,并用来求解其线性方程组.进而将其思想方法应用于块三对角矩阵行列式的计算.与现有的算法比较,此算法具有计算量和存贮量较少,且编程较简单的特点.     

Jacobi矩阵逆特征问题存在唯一解的条件

（?）1.引 言设n阶Jacobi矩阵为记Jp,q为Jn的主子矩阵;即 关于Jacobi矩阵逆特征值问题的研究文献很多,类型有由两组谱数据或两个特征对（指特征值及相应的特征向量）构造Jacobi矩阵的元素[1].由主子阵及一组谱数据构造Jacobi     

用割线法迭代求解对称三对角矩阵特征值问题

为对称三对角矩阵特征值问题，提出一种新的分而治之的算法。新算法以二分法，割线法迭代为基础，不同于Ｃｕｐｐｅｎ的方法和Ｌａｎｇｕｅｒｒｅ迭代法。理论分析和数据实验的结果表明：新算法的收敛速度明显比文［１］中的Ｌａｇｕｅｒｒｅ迭代法快。     

对称矩阵三对角化的混合并行算法设计

基于Householder转换,给出了稠密对称矩阵三对角化的MPI＋OpenMP混合并行算法。内容集中在SMP集群系统环境下算法的负载平衡、通信开销和性能评价。OpenMP共享内存并行采用了粗粒度方法,解决了MPI算法中的负载平衡问题,降低了通信开销。在深腾6800上的试验结果表明,MPI＋OpenMP版本比纯MPI版本具有更好的性能和可扩展性。     

The reconstruction of a specially structured Jacobi matrix with an application to damage detection in rods

A finite-element discretization of the differential equation for the axial vibration of a rod with varying cross-section leads to a specially structured n × n matrix pencil. The reconstruction of this pencil from its spectrum can be achieved by the reconstruction of a unique Jacobi matrix using half of its spectrum and half of the spectrum of its principal submatrix of order (n − 1). The technique is used in an optimization problem formulated for damage detection in rods defined in terms of changes in the effective cross-sectional area.     

双反对称矩阵反问题解存在的条件

112 数值计算与计算机应用2002年51.问题的提出矩阵反问题及逆特征值问题在工程中应用广泛,关于它们的     

Numerical Solution Of Inverse Problem For Elliptic Pdes

This work is concerned with computing the solution of the following inverse problem: Finding u and 𝜌on D such that: $$\nabla \cdot (\rho \nabla u) = 0,\quad \hbox{on}\ D;$$ $$u = g,\quad \hbox{on}\ \partial D;\qquad \rho u_n = f,\quad \hbox{on}\ \partial D;$$ $$\rho (x_0, y_0) = \rho_0,\quad \hbox{for a given point}\ (x_0, y_0) \in D$$ where f and g are two given continuous functions defined on the boundary of D , and D is a given bounded region of R 2 . The solution is found using a development of the direct variational method. The two unknown functions are represented by linear combinations of certain classes of functions and using multiobjective optimization to minimize the two objective functionals F and H , where $$F = \vint \vint_D \rho (x,y) \nabla u\cdot \nabla u\,\hbox{d}x\,\hbox{d}y\quad \hbox{and}\quad H = \vint_{\partial D} (\rho u_n - f)^2 \hbox{d}s$$ A computer program is written and implemented and tested for data formed by numerical simulation.     

逆P-信息嵌入隐藏与它的逆P-推理分离-发现

逆P-集合(inverse packet sets)是由内逆P-集合F(internal inverse packet set F)与外逆P-集合(outer inverse packet set )构成的集合对;或者()是逆P-集合。逆P-集合是把动态特性引入到有限普通集合X内(Cantor set X),改进有限普通集合X得到的。逆P-集合具有与P-集合相反的动态特性。利用逆P-集合给出逆P-信息的概念、逆P-信息嵌入隐藏与嵌入-隐藏定理、逆P-信息的隐藏还原属性特征、逆P-信息嵌入隐藏的逆P-推理分离-发现。利用这些结果,给出逆P-信息嵌入隐藏的逆P-推理分离-发现的应用。     

Inverse scattering by a multilayered obstacle

In this paper, we consider the inverse scattering problem of a plane acoustic wave by a multilayered obstacle which is important in various areas of imaging and nondestructive testing. When the core is penetrable (with transmission boundary conditions), we obtain that the core is determined uniquely by the corresponding far field pattern.     

Inverse electroencephalography for volumetric sources

In this work the problem of recovering bioelectrical sources on the cerebral volume, from measurement of the potential generated by these sources on the scalp, is studied. This problem is an ill posed problem, since given a measurement on the scalp, there are different bioelectrical sources that produce this measurement and small variations in the input data can produce significant variations in the source localization. The problem is studied through a boundary value problem, which is obtained using a model that describes the head as a conductive layer medium. This model allows relationships between the characteristics of the bioelectrical activity and the EEG to be established. We find in this work conditions under which the inverse solution is unique and we give an algorithm to find it. In the simple case, when the head is modeled through two concentric circles, we give a regularization strategy.     

一个反求Bezier曲面控制点的算法

本文将反求m×n次Bezier曲面控制点问题,转化为求解m+1个n+1阶线性方程组和n+1个m+1阶线性方程组问题。这些线性方程组的系数矩阵是著名的Vandermonde矩阵。通过求解Vandermonde矩阵的逆矩阵,使CAD/CAM曲面造型中常常遇到的反求Bezier曲面控制点问题得到有效的解决。同时本文给出了一种求解Vandermonde矩阵的逆矩阵的方法。     

逆P-推理与未知信息推理-搜索与发现

逆P-集合(inverse packet sets)是改进P-集合(packet sets)得到的一个新的数学结构,它是由内逆P-集合X珡F(internal inverse packet setX珡F)与外逆P-集合X珡F珚(outer inverse packet setX珡F珚)构成的集合对;或者(X珡F,X珡F珚)是逆P-集合。逆P-集合具有动态特性,逆P-集合的动态特性与另一类信息系统的动态特性相同。P-集合是把动态特性引入到有限普通集合X内,改进有限普通集合X得到的。P-集合具有动态特性,P-集合的动态特性与一类信息系统的动态特性相同。P-集合在一类信息系统中获得了多个应用。P-推理(packet reasoning)是P-集合生成的一个具有动态特性的推理。利用逆P-集合(inverse packet sets)与逆P-推理(inverse packet reasoning)给出逆P-推理与内-外搜索定理、逆P-推理的几何特征,以及逆P-推理与未知信息搜索-辨识的多个基本理论结果与应用。逆P-集合与逆P-推理具有好的应用前景。     

Inverse Dynamics of Flexible Manipulators with Coulomb Friction or Backlash and Non-Zero Initial Conditions

An algorithm is presented for computing non-causal inverse dynamics for nonlinear noncollocated systems with non-zero initial conditions. A noncollocated system has a controlled degree of freedom not collocated with an actuator. Inverse dynamics is the process of computing actuator inputs to obtain desired responses at the controlled degrees of freedom. The algorithm uses an iterative frequency domain approach in computing the inverse dynamics. The algorithm is demonstrated via computer simulations of a flexible manipulator with Coulomb friction in one case, backlash in another case, and non-zero initial conditions in both cases.