查询词典 iterative method for eigenvalue problems

This paper discusses inverse problems of secondary eigenvalue for anti-skew-symmetric matrices on a linear manifold.

讨论了线性流形上次反对称矩阵的次特征值的反问题，给出了解存在的条件，并给出了解的通式。

This paper deals with the non - linear eigenvalue problems arising from dynamic finite element in structural analysis.

本文研究结构分析中动态有限元引起的非性特征值问题。

The paper deals with the existence of nontrivial solution s to a class of nonlinear Hammerstein eigenvalue problems using the cone theory and the topological approach.

运用锥理论和拓扑方法研究一类非线性Hammerstein本征值问题的非平凡解。最后，把抽象结果应用于研究Lidstone本征值问题的非平凡的存在性

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

The numerical calculation commonly used for the Delphi process more than 100, including solutions of linear algebraic equations, interpolation, numerical integration, special, function approximation, eigenvalue problems, data fitting equation Root and solve nonlinear equations, functions and the extreme optimization, statistical data description, Fourier transform spectra, solution of ordinary differential equations reconciliation partial differential equations.

本书共有数值计算中常用的Delphi子过程100多个，内容包括解线性代数方程组、插值、数值积分、特殊函数、函数逼近、特征值问题、数据拟合、方程求根和非线性方程组求解、函数的极值和最优化、数据的统计描述、傅里叶变换谱方法、解常微分方程组和解偏微分方程组。

These results are applied to solve a class of inverse eigenvalue problems for real matrices with a submatrix constraint and the expression of general solution and best approximation are also given.

最后，将所得的结果应用于子阵约束下实矩阵特征值反问题的最小二乘问题，得到了该问题解的表达式与最佳逼近解。

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。

Two new eigenvalue problems and corresponding soliton hierarchies are derived, in which two typical equations are the generalized coupled Korteweg-de Vries and the generalized equations.

我们着重对两个新的保谱问题导出与之相联系的两族新的孤子方程，其中典型的是新的广义耦合KdV方程和新的广义TD方程。

Traditional sports teaching method,already could not adapt the new times sports curriculum to reform; this article means which through the literature law, the questionnaire investigation law, the cut-and-try method unifies, carries on the comparison to the traditional each sports teaching method, discovered the sports competition teaching method can adapt the new times student sports demand; the competition teaching method is unifies the traditional teaching method in the foundation one new teaching method, proved through the experiment, its teaching effect is good.

一些传统的体育教学思想、教学理念、教学方法、教学模式已经不能够适应现代教学的需要，在此过程中，为提高教学质量，就必须对教学方法进行改革。作为体育教学，如何进一步转变体育教育思想，深化体育教学改革，摆脱旧的传统的教学体系、思想体系和理论模式，逐步形成一个新型的，具有中国特色的教学过程和教材体系，使我国体育教学面向未来社会的需要，跟上21世纪学校体育发展的需要，是本文探讨和研究的问题。

Among used machine learning methods, the gradient descent method is widely used to train various classifiers, such as Back-propagation neural network and linear text classifier. However, the gradient descent method is easily trapped into a local minimum and slowly converges. Thus, this study presents a gradient forecasting search method based on prediction methods to enhance the performance of the gradient descent method in order to develop a more efficient and precise machine learning method for Web mining.However, a prediction method with few sample data items and precise forecasting ability is a key issue to the gradient forecasting search method. Applying statistic-based prediction methods to implement GFSM is unsuitable because they require a large number of data items to model a prediction model. In the contrast with statistic-based prediction methods, GM(1,1) grey prediction model does not need a large number of data items to build a prediction model, and it has low computational load. However, the original GM(1,1) grey prediction model uses a mathematical hypothesis and approximation to transform a continuous differential equation into a discrete difference equation in order to model a forecasting model.

其中梯度法是一个最常被使用来实现机器学习的方法之一，然而梯度法具有学习速度慢以及容易陷入局部最佳解的缺点，因此，本研究提出一个梯度预测搜寻法则(gradient forecasting search method， GFSM)来改善传统梯度法的缺点，用来提升一些以梯度学习法则为基础的分类器在资讯探勘上的效率与正确性；而一个所需资料量少、计算复杂度低且精确的预测模型是梯度预测搜寻法能否有效进行最佳解搜寻之关键因素，传统统计为基础之预测方法的缺点是需要较大量的数据进行预测，因此计算复杂度高，灰色预测模型具有建模资料少且计算复杂度低等优点，然而灰色预测理论以连续之微分方程式为基础，并且透过一些数学上的假设与近似，将连续之微分方程式转换成离散之差分方程式来对离散型资料进行建模及预测，这样的作法不尽合理，且缺乏数学理论上的完备性，因为在转换过程中已经造成建模上的误差，且建模过程仅考虑相邻的两个资料点关系，无法正确反应数列未来的变化趋势。

The two-acre Dunbar Community Garden in Little Rock has served as a model for several years.

几年来，坐落于小石城，占地两英亩的邓巴社区菜园树立了一个标杆。

Jerry points to the jacket hanging in the bathroom. It's ruined, and unwearable What?

杰瑞指着洗手间里挂着的夹克，毁了，不能穿了）什么？