逼近

The arc data interpolation error by secant, tangent and chord, and the smallest error by secant mode is analyzed in this paper. The relation between the maximum radial error and arc radius and approach step-length in the secant mode of arc data interpolation in CNC system is detailed.

在分析数控系统圆弧数据插补割线方式较切线、内接弦插补方式误差更小的基础上，讨论了数控系统圆弧数据插补割线方式中最大径向误差与圆弧半径和逼近步长的关系。

With the interpolation, resulting nearly arc length parameterized curve interpolatesa set of points of original curve.

最后，两个实例表明了近似弧长参数化曲线能很好地逼近原曲线，且没有所不希望的波动。

Two calculating methods of straight line and Archimedes spiral approximating involute are introduced.

介绍了用直线及阿基米德螺旋线逼近渐开线的两种方法。

One bases on function value and another bases on arithmetic average difference quotient. In this paper, the author mainly studies the approximation properties of both the function value and the derivative of two kinds of splines interpolation mentioned before, and the optimal error constants are obtained finally.

文中分别就这两类插值样条的函数值及一阶导数的逼近性质展开讨论，相应得出这两种插值函数在被插函数分别为一阶连续可导和二阶连续可导情况下的最佳误差常数。

According to the approximation ability of WNN, the nonlinear system is able to be modeled, obvious effect was shown in process modeling of residuum cracking and prediction of asphaltum yield and pyrolysis gas yield.

利用小波网络的逼近性，对非线性系统进行建模和预测，通过渣油裂解的实例，将小波网络与RBF网络作为对比，可以看出，小波网络的建模和预测效果都优于RBF网络。

Stability and astringency of the identified model are...

仿真试验表明模型具有快速准确的逼近能力和很好的泛化能力。

Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators.

Gupta等给出了有关这类算子点态逼近的速度、 Voronovskaja型渐近公式以及一些正结果。

We introduce the general sigma point selection framework, and give two kinds of efficient methods: a reducing the computing complexity by decreasing the number of the sigma point; b scaling the sigma points to influence the effects of the higher order moments, then improve the accuracy of the UT; c Convergence analysis of the UKF, when used as an observer for nonlinear deterministic discrete-time system, is presented. Based on the UKF that captures the posterior mean and covariance accurately to the second or third order term (in terms of Taylor series expansion) for any form of nonlinearity, sufficient conditions to ensure local asymptotic convergence are established.

论文介绍了sigma点的一般选取规则，并给出了两种有效的方法：a通过减少sigma点集合的元素的数目来减少计算复杂度，b通过增加参数来逼近泰勒展开的高阶项，从而提高UT变换的精度；c论文研究了UKF算法应用于非线性确定性离散时间系统时的收敛性问题。

Firstly, the Voronovskaja type formula of asymptotic expansion of this kind of operators is given. Then the approximation of the bounded variation functions by the kinds of operators is discussed.

第一节给出该算子的Voronovskaja型渐近展开公式；第二节讨论该算子对有界变差函数的逼近。

In the second chapter,we establish the weakly asymptotic order of the classical Bernstein interpolation sequence approximate functionin the Wiener space(or 1-fold integrated Wiener space).

第二章给出了经典的Bernstein多项式算子列逼近函数时在Wiener空间(或1-重积分Wiener空间)下的平均误差的弱渐近阶。

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。