浅议双线性函数在不同基下的矩阵间的关系

在双线性函数的概念之下将矩阵合同与相似的关系统一起来,并将二次型与内积也统一到双线性函数之下。     

模态综合超单元法的简化解

在子结构的固定对接界面最低频率比整体结构基频较高的条件下,导出了模态综合超单元法的简化解.通过数值运算,充分说明了本方法经济有效、精度令人满意.     

非对称矩阵结构系统固有值分析的广义逆迭代法

本文提出一种求解非对称矩阵结构的固有值的数值方法-通过广义的逆迭代过程把一个大型非对称的二次特征值问题简化为小型的标准特征值问题.算法不涉及复数运算,也不需把n阶的二次问题变换为2n阶的线性问题.迭代是在原n阶规模上进行,从而保持了系统各矩阵稀疏、带状的特点.节省了存储量和计算机时.数值实验表明本方法具有良好的稳定性和精度.     

Z-矩阵最小特征值及特征向量的数值算法

基于Z-矩阵与非负矩阵的关系,给出了不可约Z-矩阵最小特征值及特征向量的同步数值算法,数值实验表明算法是可行有效的。     

完成具有特定最小最大特征值的Jacobi矩阵(英文)

通过使用Jacobi矩阵的各阶顺序主子阵特征多项式之间的递推关系,解决了具有特定最小最大特征值的Jacobi矩阵完成问题.证明了这个矩阵完成问题存在唯一解的充要条件,得到了被插入元素的递推表达式.然后利用这些结果解决了具有2n 1个极端特征值的Jacobi矩阵的逆特征值问题.最后,提出了确定Jacobi矩阵的相应算法.数值实验验证了这些算法的有效性.     

四元数矩阵的对角化及其算法

四元数矩阵的对角化在四元数力学等四元数应用学科的理论研究和数值计算中起到重要的作用。本文通过引入友向量的方法,进一步研究了四元数矩阵的对角化问题,构造性地给出了四元数矩阵对角化的实用算法。     

一类函数f(x_1,x_2,...,x_n)=X~TA~nX+αX的最值问题

研究一类函数f(x_1,x_2,…,x_n)=X~TA~nX+αX的最值问题,回答f什么时候有最值及最值是多少。     

非奇异三对角矩阵的显式逆

三对角矩阵的可逆性在应用线性代数的不同领域有着广泛的应用。本文给出一般非奇异的三对角矩阵的逆矩阵的求解公式。其结果极大的改进了与三对角矩阵的逆矩阵有关的几个著名的结果,并且三对角矩阵的逆矩阵也容易计算。     

EMD与JADE相结合的算法及验证

针对汽车变速器齿轮在长时间高强度工作状态下易产生故障的问题,提出了一种基于经验模式分解(EMD)和盲源分离算法中的特征矩阵联合近似对角化法(JADE)相结合的汽车变速器齿轮故障诊断算法.首先,将振动信号进行EMD分解,再根据互相关准则对分解后的本征模分量进行重构,构造虚拟噪声信号,并以此作为JADE的输入矩阵;然后,采用JADE算法分离得到能清晰反映齿轮状态的特征信号.最后将该方法应用于汽车变速器齿轮故障诊断中,仿真和实测分析结果均表明该方法有效可行.     

反自反矩阵的二次特征值反问题及其最佳逼近

二次特征值反问题是二次特征值问题的一个逆过程,在结构动力模型修正领域中应用非常广泛．本文由给定的部分特征值和特征向量,利用矩阵分块法、奇异值分解和Moore-Penrose广义逆,分析了二次特征值反问题反自反解的存在性,得出了解的一般表达式．然后讨论了任意给定矩阵在解集中最佳逼近解的存在性和唯一性．最后给出解的表达式和数值算法,由算例验证了结果的正确性．     

Perturbation Bound for the Eigenvalues of a Singular Diagonalizable Matrix

In this short note, we present a sharp upper bound for the perturbation of eigenvalues of a singular diagonalizable matrix given by Stanley C. Eisenstat [3].     

Phase-shifting interferometry by a similar matrix 1-norm algorithm

Phase-shifting interferometry (PSI) is an effective technique in optical measurement. In this paper, a noniterative algorithm for retrieving the unknown phase shifts in three frame generalized PSI is proposed, in which the interference term of each frame is eliminated by the aid of a reference interferogram with the phase shift of π. With this algorithm, the phase shifts can be determined by solving a system of transcendental equations with trigonometric functions, in which this system consists of three different ratios between the similar matrix 1-norms of the intensity difference and the intensity sum. After the determination of phase shifts, a phase can be retrieved easily. The algorithm provides a possible method to solve the limitation of the fringe number existing in some common algorithms. The feasibility and accuracy of this algorithm were demonstrated by the simulation and experimental results.     

浮游植物活体三维荧光光谱特征提取

测量了6种东海常见的浮游植物在两个温度(20℃,15℃)、三个光照(7000Lux,4100Lux,1100Lux)下的不同生长期的三维激发／发射荧光光谱,研究了光谱特征提取方法。对去除散射干扰后的三维光谱进行了奇异值分解,得到的相应于激发光谱的第一主成分具有区分藻种的能力,可作为三维光谱的特征光谱。分析结果表明,实验条件下,等鞭金藻(Isochrysis galbana)、岛国大扁藻(Platymonas helgolanidica)和中肋骨条藻(Skeletonema costatuma)的特征光谱相似度高,塔玛亚历山大藻(Alexandrium tamarense)、东海原甲藻(Prorocentrum dentatum)和尖刺拟菱形藻(Pseudo—nitzschia pungens)光谱相似度稍差。     

用传递矩阵法分析微穿孔板的声学特性

微穿孔板吸声结构以其众多的优点,在噪声控制领域得到越来越广泛的应用。因微穿孔板结构中涉及大量的参数,在穿孔板层数较多时,用声电类比法或试验的方法研究微穿孔板结构的吸声性能将变得非常复杂。传递矩阵法尤其适于多层结构的分析,且易于用计算机编程实现。文章推导了用传递矩阵法计算微穿孔板结构声学性能的计算公式,并与用声电类比法计算的结果、试验测定数据进行了对比,结果显示,传递矩阵法是可以作为微穿孔板结构设计的一种简单而有效的参考方法。     

Recursive formulae for wave propagation analysis of FGM elastic plates via reverberation-ray matrix method

Through a laminated plate model, a recursive formulation for the method of reverberation-ray matrix (MRRM) is proposed for the analysis of free wave propagation in an elastic plate with material properties varying along the thickness direction. In contrast to the traditional MRRM, the present new formulation behaves well for high frequency computation, while the heavy computational cost of storage and memory can also be cut down. Numerical examples are given to analyze dispersion characteristics of waves in FGM plates, and the comparison among traditional MRRM and the recursive formulation demonstrates the significant efficiency of the proposed recursive formula.     

Motion of an elliptical void in interconnects embedded in matrix under gradient stress field

We present an analytical solution for the motion of an elliptical void in representative interconnects embedded in a matrix with different line aspect (volume) ratio, under gradient stress field. An orthotropic elastic model is used to represent representative interconnects embedded in a matrix. The effects of stress gradient, stress states, an equivalent void size, the orthotropic material characteristic, and the shape parameter of the void on the motion velocity of an elliptical void are described and discussed.     

Integrated scheduling algorithm based on an operation relationship matrix table for tree-structured products

The processing and assembly of tree-structured products can be performed simultaneously, which leads to an integrated scheduling problem. To address this problem, we propose an integrated scheduling algorithm based on an operation relationship matrix table. The algorithm initially establishes an operation relationship matrix table. The improved genetic algorithm based on the table is subsequently adopted to solve this problem. To ensure that the initial population satisfies the sequence constraints, this algorithm uses a novel encoding method based on the dynamic operation relationship matrix table. In addition, corresponding new crossover and mutation methods are designed to ensure the feasibility of the generated offspring individuals. A simple decoding method based on the operation relationship matrix table is also presented. The feasibility and superiority of the proposed algorithm is demonstrated experimentally. Some existing algorithms have defects, such as scale limitation, indispensable repair process and incomplete encoding. However, the proposed algorithm not only overcomes such defects but also significantly reduces the complexity of addressing the problem, which can provide valuable references for solving similar problems.     

高温蒸汽管道蠕变损伤检验中孔洞的识别与判断

提出了孔洞识别的四项补充原则，有助于蠕变孔洞的识别与判断。分析了孔洞的形态及分布特征，对这些孔洞特征进行了实际描绘。     

Combinatorial relaxation algorithm for the maximum degree of subdeterminants: Computing Smith-Mcmillan form at infinity and structural indices in Kronecker form

LetA(x)=(A _ij (x)) be a matrix withA _ij (x) being a polynomial or rational function inx. This paper proposes a combinatorial relaxation type algorithm for computing the highest degree _k (A) of a minor ofA(x) of a specified orderk. Such an algorithm can be used to compute the Smith-McMillan form of a rational function matrix at infinity, as well as the structure of the Kronecker form of a matrix pencil. The algorithm is based on a combinatorial upper bound on _k (A), which is defined as the maximum weight of a matching of sizek in a bipartite graph associated withA. The algorithm is efficient, making full use of the fast algorithms for weighted matchings. It is combinatorial in almost all cases (or generically) and invokes algebraic elimination routines only when accidental numerical cancellations occur. The validity relies on the integrality of bipartite matching polytopes.This work is supported in part by the Sumitomo Foundation.