近似方法

Meshless method is a new numerical method on problem for determining solution of partial differential equation. It is an approximation method based on nodes, and doesn't need a mesh entirely or partly. Then the discontinuous problems, the extremely large deformations problems, and movable boundary problems, etc, can be solved by use to meshless without the re-meshing techniques. And not only the calculated precision can be guaranteed, but also the calculated difficulty can be decreased.

无网格方法是求解微分方程定解问题的一种新的数值方法，它采用基于点的近似，可以彻底或部分地消除网格，因此在处理不连续、大变形、移动边界等问题时可以完全抛开网格重构，不仅可以保证计算的精度，而且可以减少计算难度。

Through the comparison with other learning methods, the conclusion is drawn that the Powell method in which the derivative is replaced by the difference quotient is an eff...

通过与其他学习算法的比较，得出结论：其中用差商近似代替导数的Powel法是一种高效、快速的学习方法，其学习速率比带动量项的学习率自适应的BP算法高一个量级，而比DavidenFletcherPowel、BroydenFletcherGoldfarlShanno等变尺度方法以及其他非线性最小二乘法的稳定性要好得多。

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。

In final chapter, we will discuss a perturbation method to solve the one-dimension Fokker-Planck equation with a constant diffusion coefficient and time-dependent drift coefficient.

所以我们在论文最后介绍一种新的方法来处理某一种Fokker-Planck方程式，这个方法就是微扰近似法。

In the paper, the theory and methodology of amplitude correction method using average of several points in discrete spectrum, which is suitable for analyzing the dynamic signals of rotating machinery with small varying speed, is proposed and systematically studied.

系统而完整地提出了处理变速机械弱时变响应信号的离散频谱多点平均幅值修正法的理论和方法，严格证明了该方法能精确地计算出平稳信号和频率微弱波动信号的幅值，能近似地计算出幅值和频率均微弱波动的信号的平均幅值，并应用这套理论成功地解释了频率微弱波动信号的幅值谱表现出较严重的"功率泄露"效应的原

In the PFD, both the differentials and non-differential terms in the differential equation are discretized, and the coefficients of the power series are determined by means of eliminating the truncation error of the corresponding modified scheme, then the high accurate difference scheme is obtained.

摄动有限差分方法在微分方程的差分近似中，离散微商项的同时，也离散非微商项，把非微商项摄动展开成网格步长△x的幂级数，并通过提高差分格式相应修正微分方程误差阶的方法求出摄动幂级数系数，从而获得高精度差分格式。

In view of the demand of computerized eye-glasses-wearing system, an approach to match two dimensional (2D) human head images with 3D glasses frame graphics in 3D space has been proposed. First, the operator points out three or six key points, which are used to locate 3D eye-glasses frame, on the human face image displayed on the computer screen interactively.

论文针对计算机化眼镜配戴系统的要求，提出了一种在三维空间匹配二维人头图象和三维眼镜图形的方法，即通过人机交互方法，由操作者在显示于计算机屏幕上的二维人头图象上，指出确定三维眼镜位置的三个或六个关键点的二维坐标及其三维对应点，从而可以近似求出人面朝向及视点坐标，再用相应位置上的三维通用人头图形替换二维人面图象，计算人面和眼镜间的遮挡关系并显示，从而完成二者的空间匹配。

The stability and convergence for spectral methods and spectral element methods are presented, with the aid of the knowledge of functional analysis and calculus and with the help of the theorem of Lax-Milagram, the stability and convergence for steady problems, evolution equations and Navier-Stokes Equations are analyzed in detail.

利用泛函分析和微积分的基本知识，运用Lax-Milagram定理等，从理论上比较详细地分析了谱方法和谱元方法在定常问题、非定常问题以及求解Navier-Stokes方程方面的稳定性和收敛性问题，得出了Navier-Stokes方程谱近似的稳定性条件和收敛性准则。

During the simulation, themost important problem is to compute the geodesic distance as fast and exactly as possible. We modify the approximating method and make it work for the concave andmultiple sources.

在这个模拟方法中，使用了改进的近似快速计算三角网格上测地距离的方法，使之能处理凹面及多源点的情况。

Optimal control of DSS formation adjusting based on Hamilton Mechanics and generating function method was investigated. An iterative way of solving the two-point boundary value problem induced by optimal control by relative motion generating function approximation was proposed.

基于考虑J_2项的DSS相对运动Hamilton力学模型和生成函数方法研究了DSS构形调整的最优控制问题，提出了求解最优控制两点边值问题的相对运动生成函数近似迭代方法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。