查询词典 jacobian method of eigenvalue problem

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

First we prove that 0 is an eigenvalue of the operator with geometric multiplicity one,next we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator,last we prove that 0 is an eigenvalue of the adjoint operator of the operator.

首先证明0是对应于该排队模型的主算子的几何重数为1的特征值，其次证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，然后证明0是该主算子共轭算子的特征值。

Sparse eigenvalue analysis technique, which makes full use of sparsity of augmented state matrix during small disturbance stability analysis for large scale power system, can compute out concerned eigenvalue subset from all eigenvalues and can analysis power systems that have arbitrary scales.

论文的主要研究工作和创新性成果如下：1针对传统特征值分析方法仅适用于中小规模电力系统的局限性，结合Prony和稀疏特征值算法，提出了一种大规模互联电网区间低频振荡分析的实用方法。

This paper studys the stability of nonlinear systems in two particular critical cases. In a case, the linear systems at the equilibrium point of interest is assumed to possess a simple zero eigenvalue. In the other case, it is assumed to possess a complex conjugate pair of simple pure imaginary eigenvalue.

本文基于中心流形定理研究了非线性系统在两种特殊临界情形下的稳定性问题，一种是与它相应的线性系统在平衡点仅有零特征根，另一种是与它相应的线性系统在平衡点仅有一对共轭的纯虚数特征根。

We then diagonalize the matrix C and obtain the eigenvalue spectrum and eigenvectors. The large eigenvalues which go beyond the upper bound of the random matrix, i.e., the Wishart matrix, reflect the local correlations between stocks. The largest eigenvalue corresponds to the market mode, and next large eigenvalues represent the interactions between stocks in a same sector.

进一步，通过对角化，我们得到矩阵C的特征值谱和特征向量，超过随机的Wishart矩阵特征值谱上边界的特征值反映了股票间的局域关联，其中最大的特征值对应于市场模式，其余的次大特征值代表了同一板块内股票间的相互作用。

This thesis analyzes the energy eigenvalue and of the Harmonic oscillator with a one-dimensional δ-function, makes a comparative study of those of the one-dimensional harmonic oscillator, and analyzes the reason which causes their different quality and the different influences to the eigenvalue of the even parity energy and to the wave function when the number of the "Z" is different.

本文研究了一维δ势场中的谐振子的能量本征值及其本征波函数，并与一维谐振子的能量本征值和波函数进行了比较，分析了它们的性质不同的原因以及取不同势参数Z值时对偶宇称能量本征值和波函数的不同影响。

There are all kinds of inverse eigenvalue and generalized inverse eigenvalue problems in the fields of structural design, vibration system, automation control and matrix decision etc.

在结构设计、振动系统、自动控制、矩阵对策等领域中存在各种各样的矩阵逆特征值问题及广义逆特征值问题。

Firstly, we give a new upper bound of a mixed graph′s largest Laplacian eigenvalue, which is more precise. And also we give a lower bound of a mixed connected graph′s largest Laplacian eigenvalue.

首先给出了混合图的最大Laplace特征值的一个新的上界，并且用实例说明我们的结果与以往结果相比更精确，同时也给出了一个连通混合图的最大Laplace特征值的一个新的下界。

To find some useful eigenvalue in time series by mining the distributing values of original series, and deduce a collection of candidate slide-window size, find the optimal slide window size by adapting to the series eigenvalue variable motion movement.

通过对时序特征值分布函数挖掘，发现时间序列中的有效特征点，进而确定一组合适的滑动窗口宽度；最后根据序列的变化情况来决定最优的滑动窗口宽度，对原数据维度进行简约。

Under the condition of knowing zero eigenvalue algebraic multiplication ,the authors have discussed the use and necessary relationship between matrix zero eigenvalue algebraic multiplication and matrix rank.

在已知零特征值代数重数时，给出了矩阵零特征值代数重数与矩阵秩之间的内在必然联系，及其一般应用。

In the chapter 2, the theoretic knowledge about the photosensitive resin and the grinding tools was firstly introduced.

第二章阐述了光固化树脂结合剂磨具的相关理论研究。

Do not use the program's indenting or margin-setting features; these will be added during typesetting.

不要使用缩排，页面边缘设置之类的选项，偶看不大懂。