函数值

In Chapter 2, one kind of rational cubic spline interpolation with linear denominator has been proposed, whose derivatives are replaced with accurate derivative values, difference quotient and arithmetic average difference quotientrespectively.

第二章给出了一类分母为线性的有理三次插值函数，当其导数值分别取为导数的精确值，一阶差商，以及算术均差商时，便得到三种插值格式，分别为给定导数值的有理三次插值函数，基于函数值的有理三次插值函数，以及基于算数均差商的有理三次插值函数。

The paper simply introduced the basic principle of surface nuclear magnetic resonance and computed the numerical integral of nuclear magnetic resonance kernel function which contained double Bessel functions using the method of Gauss quadrature and continued fraction expansion, and then discussed influence of conductivity to nuclear magnetic resonance′s signal.

简要介绍了地面核磁共振找水的正演理论方法，采用高斯求积并结合连分式展开的方法对核磁共振核函数中包含双重贝塞尔函数的积分核进行了数值积分，进而计算出精度较高的核函数值，在此基础之上，讨论了导电性对地面核磁共振信号的影响。

However, to establish global convergence for these latter methods, one must enforce either sufficient decrease conditions (the Armijo-Goldstein-Wolfe conditions)or a fraction of Cauchy decrease condition - all of which rely on explicit numerical function values, as well as explicit approximations to the directional derivative at the current iterate.

但是，为了保证后面方法的全局收敛，必须有足够的减少条件（Armijo-Goldstein-Wolfe条件）或者部分柯西减少条件——它们全都依赖于外在的数值函数值，就和在当前迭代逼近方向导数一样。

In this paper, we propose an algorithm for finding global minimization by discrete mean value-level set, the convergence of this algorithm is proved, a termination rule and some numerical examples are given.

西文提出了一个只需计算函数值的离散均值—水平集求全局最优的方法，给出了算法的终止准则，证明了算法的收敛性，并给出了某些数值例子。

The formula requires not only the function value,but also the first derivative and second derivative value on node.

此类求积公式不但需要结点上的函数值，还需要结点上的一阶和二阶导数值。

To solve above problems, a new method has been created in this paper: to construct a Hermite polynomial approximation of the objective function by FE solution using the sensitivity idea.

因此，本文提出在进行若干次电磁场数值计算之后，利用目标函数值和目标函数对设计变量的灵敏度建立目标函数的计算方法。

Finally numerical examples with three shape functions are analyzed in detail. The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also one or higher orders derivative.

最后，通过多个数值算例的计算比较了三种形函数的计算结果，结果显示本文提供的MGMLS方法关于函数值和各阶导数值都具有很高的精度。

Aimed at the calculation complexity of Newton iterative method for solving nonlinear equation,a new iterative method with higher convergence rate and without derivative calculation is presented in this paper.Its convergence rate p is 1.839 and it doesn't need to calculate derivative.

为解决Newton迭代法求非线性方程数值解时必须提供一阶导数值的问题，提出了一个新的迭代方法，该方法不需提供导数值而只需计算函数值，且具有p=1.839的收敛阶，因而是一个收敛速度快且不需要计算导数值的迭代方法。

The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also first or higher orders derivatives.

数值计算显示本文提供的方法关于函数值和各阶导数值都具有很高的精度。

Furthermore the numerical flux from the Riemann solver is delicately expressed in a compact manner, say by the well known Godunov flux function, which paves the way to full investigation of numerical approximations.

由上述的Riemann解所提供的数值流通量经仔细验证后可以被简洁地表示为Godunov流通量的函数值，这为研究一般意义下的数值逼近铺平了道路。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。