查询词典 eigenvalue problem

In this paper, the elemntary knowledge of oblique circulant matrix is described briefly and three inverse eigenvalue problems which a-re denoted by Ⅰ,Ⅱ,Ⅲ and best approximation problem which is denoted byⅣ on oblique circulant matrix are presented.

本文介绍了斜循回方阵的基本内容，提出了斜循回方阵的特征值反问题Ⅰ，Ⅱ，Ⅲ及其最佳逼近问题Ⅳ，给出了它们有解的充分必要条件及求解算法，并举出了相应的数值例子。

The eigenvalue assignment problem is a classical problem in control systems.

在控制理论领域里，特征值配置问题是一个经典问题。

Based on the concept of secondary eigenvalue and secondary eigenvector, the author gives the model for the inverse problem of secondary eigenvalue of the matrix, discusses the inverse problems of secondary eigenvalue for anti-skew-symmetric matrices on a linear manifold.

在第三章中，本文对矩阵的一类逆特征值问题进行了研究，针对次特征值、次特征向量概念，提供了矩阵的逆次特征值问题模型，讨论了一类线性流形上次反对称矩阵的逆次特征值问题。

Based on a general parametric eigenstructure assignment result proposed for descriptor linear systems via proportional plus partial derivative state feedback and a result for generalized eigenvalue sensitivity problem of matrix pairs, parametric representation of the closed-loop eigenvalue sensitivities to the perturbed elements in the open-loop system matrices is obtained. An effective algorithm for eigenvalue assignment with minimum sensitivity in descriptor linear systems via proportional plus partial derivative state feedback is then proposed.

摘要基于广义线性系统比例与部分状态导数反馈参数化特征结构配置结果和矩阵对广义特征值灵敏度结果，得到了关于开环系统矩阵中摄动元素的闭环特征值灵敏度的参数表达式，并在此基础上提出了广义线性系统比例与部分状态导数反馈最小灵敏度特征值配置的有效算法。

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。

With the aid of the adjoint relationship of symplectic ortho-normalization and integral transformation, solutions of duality equations were obtained, or Saint-Venant solutions and local solutions, reducing the original problem to finding zero eigenvalue solutions and non-zero eigenvalue solutions.

利用辛正交归一关系和积分变换得到了对偶方程的解，即圣维南解和局部解，从而将原问题转化为寻找零本征值本征解和非零本征值本征解问题。

In chapter Ⅰ, a historial review of structure control is given; In chapter Ⅱ, A discussion of the controllability and observablity of flexible structures is given, Two kinds of controllability and observablity index are defined, and applied to actuator allocation; chapter Ⅲ considers the reduction of high order flexible structure mode; the content of chapter Ⅳ is about the basic problem of distributed parameter control system design. It is proved that a stable controllor in mode space may be unstable in real use in distributed paramater systems, also, by closed loop mode concept, a pole assignment method of flexible structure controllor design is given; chapter Ⅴ is about the low-authority controllor design, it is pointed out by use of high order eigenvalue/eigenvector perturbation, a better controllor can be designed; chapter Ⅳ considers flexible structure reduced order control; chapter Ⅶ disscusses the basic problem of flexible structure computer control, analyses discreate controllablity and observablity and its computing, the sample period and coefficient wordlength; chapter Ⅷ is on the problem of low flexibility compensation; chapter Ⅸ is a design example.

在第一章简要回顾了挠性结构控制的历史，并且指出控制中的一些问题；第二章讨论了挠性结构的能控性与能观性，定义了两类能控性程度和能观性程度指标，还将能控性程度概念应用于执行器位置的确定；第三章论述了高阶模型的降价问题，比较了适于挠性结构模型降阶的方法，指出其适用范围；第四章内容是分布参数系统设计的基本问题，首先证明在模态空间中设计的稳定的控制器在实际分布系统上可能是不稳定的，进而根据闭环模态的概念，获得挠性结构控制器设计的极点配置方法；第五章的内容是关于低权控制器的设计问题，指出利用特征值高价摄动和特征向量的摄动，可以设计出更加完善的低权控制器；第六章讨论挠性结构降阶控制问题；第七章讨论挠性结构计算机控制的基本问题，分析了时间离散化模型的能控性和能观性及其计算问题，讨论了采样周期选择和系数字长问题；第八章讨论低挠性结构的补偿问题；第九章的设计例子用来说明第二章和第四章的结果。

Based on a 2×2 eigenvalue problem, a 3×3 Lenard pair of operators and a new 1+1 dimensional soliton hierarchy are presented.

本文立足于一个2×2谱问题，获得了3×3 Lenard算子对，并由此导出一类非平凡的(1+1)维孤子方程族。

The perturbational reanalysis method of repeated eigenvalues and associated eigenvectors of the lineargeneralized eigenvalue problem is further investigated on the basis of the relevant results of previous stud-ies.

本文基于已有研究结果，进一步探讨了线性广义特征值问题的重特征值及其特征向量摄动重分析理论和方法，阐述了重特征值情形下摄动重分析方法的一些重要特点，完善了重特征值的特征向量的二阶摄动算式，并论证了重特征值摄动法与相异特征值摄动法之间的统一性。

P procedure. In our model, however, we have used a modified subband structure which is actually the solution of the eigenvalue problem in a 4×4 Luttinger-Kohn matrix.

而在我们的模型里面，我们使用了求解4×4 Luttinger-Kohn矩阵的特徵值的方法来得到修正过的次能带结构。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。