查询词典 iterative method for eigenvalue problems

Thesolutions compose self-contained inner product space (weight function is constant 1),i.e., they are basic series of Hilbert space; hence any internal waves could beexpanded into generalized Fourier series. With difference method, Sturm-Liouvilleequation is transformed to matrix eigenvalue problem. Each eigenvalue is related to ahorizontal wave number, and relevant solution is a certain mode of internal wave.

其解系构成完备的加权(权函数为1)内积空间，即Hilbert空间，从而内波现象可以展成该解系的广义Fourier级数；采用差分方法，将 Sturm-Liouville 方程转化为矩阵特征值问题，每一个特征值对应一个内波波数，该特征值对应的解则是内波的某一模态。

The eigenvalue equation for the cladding modes of the metal-coated fiber is obtained and the method of solving the complex eigenvalue equation is presented.

分析了金属包层光纤的特点，给出了金属包层光纤包层模的本征方程，并给出了这一复本征方程的求解方法。

Direct method of Gaussian elimination, Gaussian main-element elimination, and the iterative method of Jacobi iteration, Gauss - Seidel (Gauss - Seidel) iterative method is linear equations numerical solution of important ways.

直接法中的高斯消去法、高斯列主元消去法，以及迭代法中的雅可比迭代法、高斯-赛德尔（Gauss-Seidel）迭代法又是线性方程组数值求解的重要方法。

An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The subspace iterative method is used for the solution of natural frequencies and vibration modes for the free vibration of beam structures.

本研究推导元素的节点惯性力时，先将元素扰动位移表示成当前固定元素座标的扰动位移和旋转之函数，故可直接求得元素的节点惯性力，元素的一致性质量矩阵可由元素节点的惯性力对元素节点的加速度微分求得。

This paper investigates alternating iterative method and generalized alternating method for the solution of a large linear system, extend the convergence theorem and comparison theorem for generalized or alternating iterative method when the coefficient are Hermitian positive definite systems.

本文主要研究了大型线性方程组的交替迭代法及迭代法的各种变形，给出了当系数矩阵为Hermitian正定矩阵时各类迭代法的收敛原理及其相应的比较理论。

Based on the improved Atiken iterative method and dimidiate method, a new algorithm of searching zero of derivative function is given, the simulation results show that if using the new algorithm to find the zero of derivative function, the convergence speed is faster than the improved Atiken iterative method .

采用二分法预报、改进的Aitken迭代校正的方法，构造了一种求导数零点的一种新算法。新算法在迭代过程中不用计算导数，且二阶收敛。数值试验表明，该算法具有较高的精度和较大的初值选择范

From the view of initial deformation,the dual intercrossed iterative method is developed to determine the initial deformations of cables and hangers,sequential method based on initial deformations to simulate the tensioning process in batches,and converse iterative method in sequential anal.

本文从索初始变形的角度出发，针对该类结构的特点，提出了&双重交叉迭代法&确定拉索和吊杆初始变形，索初始变形&顺序分析法&模拟分批张拉施工过程以及索张拉力&顺序分析逆迭代法&解决张拉力已知时的预应力施工过程模拟问题，并将这三种方法进行不同组合，解决各种情况下的多次、分批张拉施工过程分析的问题，由此确立了一套完整的适合该类结构的预应力全过程分析方法。

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

This train classifies "information carrier adhering to the build" as design elements, and probes into integrated design method of it and single building separately: method of definite position, method of definite form and method of combination; Then, this train probes into integrated design method of it and colonys building , that bases on the cognitive design method: method of rhythm controls,method of node outstanding, and that aims at the design method to protect: method of protect original, method of repairing and method of renewal.

本文的第四部分提出了一体化设计的思路，将建筑附着信息载体作为设计元素，探讨了它与建筑单体一体化设计的方法：定位法、定形法、混合法；以及它与建筑群体一体化设计时，基于认知的设计方法：节奏控制法、节点突出法，旨在保护的设计方法：存真法、修缮法、更新法。

By using accelerating Aitken method in iterative method of nonlinear equations, a new modified method is given. The method is applied to modified Newton method, thereby a new method is developed, which is faster and stable. Also, its algorithm is given. Numerical results show that the new method is very efficient.

通过对非线性方程组的迭代法引入Aitken加速技术，设计了一种非线性方程组的迭代解法的加速方法；将该方法与M步Newton法相结合，得到一种收敛速度快而且计算稳定的方法，并给出了具体算法；数值结果表明了新算法是有效的。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。