近似导数

Thirdly, in order to improve the learning efficiency and stability of feedforward neural network, a fast learning algorithm for neural networks based on CGM-OC approach is presented. Compared with other learning methods such as BP method, Broyden Flecher Goldfarl Shanno method and Powell method in which the derivative is replaced by the difference quotient etc, simulation results show that the proposed method is an efficient and fast one.

第三，为了提高前馈神经网络权值的学习效率及稳定性，提出一种基于正交校正共轭梯度优化方法的神经网络学习算法，通过与其它学习算法（如：BP算法、变尺度法、用差商近似代替导数的Powell法等）的比较，经仿真试验表明，本算法是一种高效、快速的学习算法。

The weight values in NLSM were adjusted automatically according to target data, which allowed the measured data with different dimensions or ranges to be treated at the same level, and thus the accuracy and stability of algorithm were improved accordingly. Derivative was replaced by the difference quotient in NLSM which further improved the algorithm speed.

非线性最小二乘法的权值根据目标数据自动调整，使得不同量纲和不同数值范围的观测数据可以在同一水平上进行，提高了计算的精度和稳定性；另一方面用差商近似代替导数加快了算法的收敛速度。

In Chapter 4, we consider more complex fractional nonlinear differential equation,also using the high order approximation presented by Lubich to construct correspond-ing numerical scheme and giving the error analysis of the algorithms.

在第四章中，进一步的考虑更复杂的非线性分数阶常微分方程，同样利用的是Lubich提出分数阶导数的高阶近似，构造相应的数值格式，并给出这一算法的误差分析，即相容性，收敛性和稳定性的证明。

Application of the QA approximation to forward modeling and Frechet derivative computations speeds up the calculation dramatically.

反演过程中的正演和Frechet导数矩阵计算都应用准解析近似大大提高了计算的速度。

In Part 5, the stability of linear large-scale singular dynamic system is investigated by using the method of vector generalized Lyapunov function and the sum type of scalar generalized Lyapunov function, respectively.

首先研究线性广义系统二次型李雅普诺夫函数的存在性；然后建立按线性近似系统决定非线性广义系统稳定性的准则；进而改进广义李雅普诺夫函数法以研究广义系统的稳定性；最后提出利用非线性函数的偏导数矩阵判别非线性微分-代数系统稳定性的若干简便判据。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括：1 各种极限运算，其中包括数列极限、函数极限以及上、下极限；2 一元函数的微分学，包括微分和导数的运算法则、微分中值定理及其应用等；3 一元函数的积分和广义积分及其收敛性；4 级数及其收敛性，包括数值级数的收敛性和函数项级数的各种运算和性质；5 多元函数的微分学及其应用，其中很多方面与一元函数的微分学近似，需要注意它们之间的区别；6 多元函数的积分学，包括多重积分的性质与计算，多重积分的的应用等；7 曲线、曲面积分及其应用；8 含参变量积分的计算与性质；9 Fourier 级数及其应用，等等。

This process of approaching is crucial to the definition of the derivative and the integral in calculus

这个近似的过程影响到对导数的定义和微积分的积分

This process o f approaching is crucial to the de f inition o f the derivative and the integral in calculus

这个近似的过程影响到对导数的定义和微积分的积分

So it produces a series of approximation matrix Bk+1 to the second order derivatives of the objective function.

因此它产生了一系列对目标函数二阶导数的近似矩阵Bk+1。

This paper introduces the Taylor formula of one dollar and multi-definition, then the proof of the value from the formula, respectively, that inequality in the value of derivatives is estimated that about industry estimates, demand infinity limit, the median point of the limit function limits, approximation, function equations and so on Taylor formula to do the induction.

本文首先介绍了一元和多元泰勒公式的定义，然后分别从证明中值公式，证明不等式，导数的中值估计，关于界的估计，求无穷远处的极限，中值点的极限，函数的极限，近似计算，函数方程中的应用等方面对泰勒公式的应用做了归纳。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。