逼近

ADAMS. According to a function with STEP5 has features of continuous first and second derivative,the higher degree of approximation,etc.,we test and verify feasibility of fore-and-aft movement and turning gait of the robot. Thus a solution of the Snake-like robot motion under the ADAM...

ADAMS软件对蛇形机器人进行了从样机模型建立到运动学仿真与分析等一系列研究；并根据STEP5函数具有一阶与二阶导数连续、较高的逼近程度等特性验证了蛇形机器人前后移动和左右转弯步态可行性；找到了一种在ADAMS环境下求解机器人运动的方法，简化了理论计算，提高了设计效率。

We use wavelet neural network to construct the nonlinear cointegration function, and give the DFP algorithm for network training.

提出了利用小波神经网络逼近非线性协整函数的方法，并给出了训练小波神经网络的变尺度算法。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

The difference schema of the initial boundary value problem was converted to the step-by-step form,which was similar to the difference schema of the initial value problem.It is concluded that the difference schema satisfying the Von Neumann condition is a stable schema,and that,under the consistency condition,such stable schema is convergent.Moreover,with error estimate expression for the difference approximation to the classical solution,the linearity condition is unnecessary.

引入反投影算子将发展方程初边值问题的差分格式转化为与初值问题差分格式类似的逐步推进的形式，从而得出：满足Von Neumann条件的差分格式是稳定的格式；在相容条件下，差分格式若稳定(或满足VonNeumann条件)则格式收敛，且对古典解的差分逼近有误差估计式，不再需要线性的条件。

Since we adopt Newton interpolation of difference quotient from the discrete data pool of unequal distance node among the scaled temperature (20℃, 1000℃), aluminum purity and aluminum density, it can greatly be approached.

我们从刻画的温度( 2 0℃、1 0 0 0℃)、铝纯度与铝密度间不等距结点的离散数据集中、采用了Newton差商插值、能极好地加以逼近、从而建立了高精度的四阶非线性数学表达式、由此从该模型中给出了 2 0℃时的高纯度铝( 99 999%～ 99.99999%)的密度值，其结果令人满意。

In order to avoid the Maratos effect, the merit functions used are approximations to Fletchers differentiable exact penalty function. Global convergence is proved on some conditions, and some numerical results are given .

为避免Maratos效应，此方法采用Fletcher的光滑精确罚函数的逼近形式作为价值函数，在一定条件下证明了算法的全局收敛性并且给出数值结果。

In order to avoid the Maratos effect,the merit function s used are approximations to Flether s differentiable exact penalty function,and the algorithm updates approximations to one-sided reduced Hessian and two-sided reduced Hessian seperately.

为避免Maratos效应，我们采用Flether的光滑精确罚函数的逼近形式作为价值函数，并且分别对Lagarange函数的单边既约Hessian的近似阵和双边既约Hessian的近似阵进行校正。

Firstly, illustrate the fundamentals (differential-integral optimizing theory) of the category of algorithms briefly in the sight of differential and integral calculus. Then two examples of the category of algorithms are listed.

首先从函数逼近的角度论述了数值积分与全局最优化的关系，随后从微积分的基本原理和定积分的定义出发对该类算法的几何意义和数学基础作了简要论述；在此基础上给出了该类算法的几个具体实现。

Apply the thought of differential and integral calculus to the problem of global optimization, imitate the algorithm of digital approximation of definite integral and construct a category of algorithms that can solve global optimization with great brevity and utility.

把微积分的基本思想应用到最优化问题中，仿照定积分的数值逼近算法构造出一类简洁实用的全局优化算法-积分选择算法。

Application of FLAC and numerical differential to surface deformation observation;2. The formulas solving numerical differential and integral of discrete function arc deduced in this paper.

推导了三次样条插值在求解列表函数的数值微分与积分的公式，给出了余项估计，编写了用于求解数值微分与积分的通用程序，通过数值算例表明，三次样条在插值逼近中具有非常好的性质。

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。