逼近

Testing results are obtained by halving interval sequential method. Various problems encountered are studied and the testing programs are reliable and efficient.

本文采用二分区间逐次试验法逼近被测量真值，研究了测试中遇到的各种问题，编排了可靠高效的测试流程。

First low order approximation of generating function and approximate optimal trajectory were obtained. Then using low order approximation of generating function of Hamilton "relative motion" to the approximate optimal trajectory, improvement of the approximate optimal trajectory was iteratively made. In this way, high order approximation accuracy can be obtained by only using low order approximation, which is much cost effective in computing.

首先以较低的计算代价，获得最优控制Hamilton系统生成函数的低阶近似，得到一条近似的最优轨线，然后将最优控制Hamilton系统相对于近似最优轨线求"相对运动"，该"相对运动"仍具有Hamilton性质，利用这一"相对运动"的生成函数低阶近似，可以对近似最优轨线进行迭代修正，从而以计算代价较小的低阶近似逼近计算代价高得多的高阶近似的精度。

First, we consider an iterative algorithm of Jacobi type and the corresponding domain decomposition algorithm for a approximate quasivariational inequality system of the Hamilton- Jacobi- Bellman equation and the corresponding convergence problem.

本文研究了逼近Hamilton-Jacobi-Bellman方程的拟变分不等式组的离散问题的Jacobi型迭代算法和Jacobi型区域分解法及其收敛性问题。

Starting from the Laplace equation, the solution of Laplace equation, in spherical coor dinates, is developed for the boundary value problem approximating the local gravity field over a spherical cap——spherical cap harmonic analysis, and the spherical cap harmonic expansion with integral order but nonintegral degree and practical formulae are given.

从Laplace方程出发，提出了在球冠上逼近局部重力场的大地测量边值问题——球冠谐分析理论，给出了非整阶整次球冠谐展开和实用计算公式。

In sphere approximate, GPS/Gravity-BVP is Neumann problem over exterior spherical domains. Then the natural boundary reduction, suggested by Feng and Yu, is applied to deal with the three dimensional problems. By expansion in spherical harmonics, the natural integral equations of harmonic problems over exterior spherical domains are obtained. Meanwhile, a numerical method for solving geodetic BVP is developed.

在球近似下将GPS-边值问题转化为Neumann外问题，用自然边界元法进行自然边界归化，得到自然边界积分方程，再求自然边界积分方程的数值解，与其他边界元方法相比，自然边界元法的计算量大大减小，并且具有很好的逼近性质，能有效地处理奇异积分，是求解GPS-边值问题有效方法。

With the idea of finite approximation, we study a new solution method for the satellite altimetry problem. Our result shows that if the continental part of the earth is sphere cap, then the solution of satellite altimetry problem can be transformed into a linear system of equations with variants of the coefficients of spherical harmonic series. We prove that the linear system of equations is separated about the orders of spherical harmonic series.

研究了球界面下卫星测高问题的解法，利用有限逼近方法得到了下列结论：若陆地部分是球冠，则卫星测高问题的解可以转换成关于球谐级数位系数的线性方程组，并且位系数的阶和次是以分离形式出现的，从而确保该解法具有实用意义。

When our palm is getting closer and closer to the Wisdom Door, it can feel the heat of the center of our palm.

手掌张开掌心渐渐靠近玄关，逼近玄关时玄关可以感受到掌心的热，同时

Adopting Hermite polynomial in stead of Taylor expansion has greatly decreased the order of the high-order cross sensitivity.

利用埃 尔米特插值逼近函数代替泰勒展开式，使目标函数对几何参数高阶交叉灵敏度的阶数大为降低，减小了计算代价。

Adopting Hermite polynomial in stead of Taylor expansionhas greatly decreased the order of the high-order cross sensitivity.

利用埃尔米特插值逼近函数代替泰勒展开式，使目标函数对几何参数高阶交叉灵敏度的阶数大为降低，减小了计算代价。

The main procedures are as following: to generate small increment of parameters automatically and to calculate the FE several times and obtain the sensitivity of objective function to the parameters, and then form a Hermite polynomial approximation, the calculation of FE solutions are substitute by the calculation of polynomial approximation, so time cost decreases dramatically.

用n维埃尔米特插值技术建立设计变量在可行域上的目标函数的逼近函数；将局部寻优的梯度算法和全局寻优的随机算法结合起来，大幅度地降低寻优过程中电磁场的计算次数。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。