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     

三对角对称矩阵逆特征问题

In this paper, four inverse eigenproblems with giventhree eigenvalues and corresponding eigenvectors are considered, somenecessary and sufficient conditions under which there exists a uniquesolution for these problems are given. Furthermore some numerical algorithmsand some numerical experiments are given.     

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...     

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。     

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     

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。     

一类矩阵不定问题有解的条件

讨论矩阵不定型问题minX∈Rn×str（（C-AXB）TJ（C-AXB））。利用矩阵的Kronecker积,拉直算子和双曲QR分解,给出问题有解的充分必要条件,并在有解条件下给出解的一般表达式。     

块三对角矩阵的并行局部块分解预条件

该文首先分析了并行局部块分解预条件的特征分布,分析表明其与串行局部块分解预条件的特征分布基本相当,从而从理论上保证了利用该预条件进行并行计算时的高效性．其次分析了利用该预条件进行并行计算时影响加速比的因素,由此说明了当问题规模不大而处理机台数增加时,计算效率必然逐渐下降的原因．最后在由6台微机连成的机群系统上将该预条件与利用多分裂技术构造的多种预条件进行了比较,实验结果说明该预条件效率高于其它预条件方法．同时在某巨型机上进行的实验表明对处理机台数比较多时,该预条件也仍然很有效．     

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。     

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.     

三对角矩阵的行列式的并行计算方法

文章针对三对角矩阵,利用矩阵的Schur余子式求矩阵行列式的方法,提出了一种并行求解三对角矩阵及其逆的行列式的算法,应用该算法可以得到较好的加速度。     

A BSP Recursive Divide and Conquer Algorithm to Compute the Inverse of a Tridiagonal Matrix

In this paper we discuss a recursive divide and conquer algorithm to compute the inverse of an unreduced tridiagonal matrix. It is based on the recursive application of the Sherman–Morrison formula to a diagonally dominant tridiagonal matrix to avoid numerical stability problems. A theoretical study of the computational cost of this method is developed, comparing it with the experimental times measured on an IBM SP2 using switch and Ethernet hardware for communications between processors. Experimental results are presented for two and four processors. Finally, the method is compared with a divide and conquer method for solving tridiagonal linear systems.     

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。     

解一类Poisson方程反演问题的并行算法

本文讨论了一类特殊的Ｐｏｉｓｓｏｎ方程反演问题的数值解法和相应的并行算法。     

Inverse adaptation of a Hex-dominant mesh for large deformation finite element analysis

In the finite element analysis of metal forming processes, many mesh elements are usually deformed severely in the later stage of the analysis because of the corresponding large deformation of the geometry. Such highly distorted elements are undesirable in finite element analysis because they introduce error into the analysis results, and, in the worst case, inverted elements can cause the analysis to terminate prematurely. This paper proposes a new inverse-adaptation method that reduces or eliminates the number of inverted mesh elements created in the later stage of finite element analysis, thereby lessening the chances of early termination and improving the accuracy of the analysis results. By this method, a simple uniform mesh is created initially, and a pre-analysis is run in order to observe the deformation behavior of the elements. Next, an input hex-dominant mesh is generated in which each element is “inversely adapted”, or pre-deformed in such a way that it has approximately the opposite shape of the final shape that normal analysis would deform it into. Thus, when finite element analysis is performed, the analysis starts with an input mesh of inversely adapted elements whose shapes are not ideal. As the analysis continues, the element shape quality improves to almost ideal, and then, toward the final stage of analysis, degrades again, but much less than would be the case without the inverse adaptation. This method permits the analysis to run to the end, or to a further stage, with no inverted elements. Besides its pre-skewing the element shape, the proposed method is also capable of controlling the element size according to the equivalent plastic strain information collected from the pre-analysis. The proposed inverse adaptation can be repeated iteratively until reaching the final stage of deformation.