牛顿法

Having discussed Wallis'interpolation in great detail, the paper shows that Wallis mainly relied on incomplete induction and analogical inference to obtain his results, an approach which was key to the creation of many important algorithms during the considered period. A comparison between Wallis'method and previous interpolations is then made and the influence of Wallis' thinking style embodied in his interpolation on Newton's invention of binomial theorem is clearly revealed.

通过考察沃里斯的插值过程，指出沃里斯插值法完全是借助于不完全归纳和类比推理得到的，并与过去的插值法做了比较，最后分析了沃里斯插值法对牛顿发明二项式定理的影响。

In calculation of definite integral,beginners tend to use three methods of calculation:(1)Leibniz formula,(2)integration by substitution of definite integral,(3)integration by parts of definite integral.

在定积分计算中初学者常用的计算方法有三种：(1)利用牛顿-莱布尼兹公式，(2)定积分的换元积分法，(3)定积分的分部积分法。

In the process of arithmetic design, Newton method is used to compute power flow of network. Graph theory knowledge is used to determine all paths from generator to load. To improve efficiency, thesis use branch expunction method to optimize the node order.

在算法设计过程中，采用牛顿－拉夫逊法进行潮流计算得到系统潮流分布，利用图论原理中的路径搜索算法确定了发电机对负荷的供电路径，此外为了提高潮流跟踪的计算效率，利用了支路消去法进行节点顺序的优化。

The convergence of the traditional nonlinear equations is related to the selected initial value, but the convergence of the fixed point method is not related to it.

传统的非线性有限元方程组的数值求解法（牛顿-拉普森迭代法与共轭梯度法）只能求解单值性有限元方程，且其收敛行为与初始值的选择有关，而不动点方法在求解非线性方程组时的收敛行为不受初始值选择的影响，在大范围内是一致收敛的。

By reviewing of the existing algorithms in CGE model, such as Scarf fixed point method, Newton-Raphson method, Tatonnement method, Johanson-Euler method, projected Lagrange method, genetic algorithm and simulated annealing algorithm, this paper expound each algorithm's principle and main problems, pointed out their respective strengths and weaknesses, and finally made a detailed comparative analysis.

本文通过对现有的求解算法进行综述，包括传统的Scarf不动点算法、牛顿迭代法、Tatonnement算法、Johanson-Euler法、投影拉格朗日算法，以及近期兴起的遗传算法和模拟退火算法，扼要说明它们的求解原理及存在的问题，指出各自的优缺点并作了详尽的比较分析与探讨，对于致力于推进CGE建模与仿真求解技术瓶颈突破的研究者们具体重要的参考意义。

The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the correspo

借助非定常时间分裂法和无波动无自由参数的NND耗散格式，建立直接求解微观分子速度分布函数的有限差分数值格式；研究并发展可用于离散速度坐标点选取和离散速度空间宏观取矩的高斯─埃尔米特无穷积分方法、等均间隔的牛顿─柯斯复合积分法、以勒让德多项式的根为积分结点的高斯─勒让德数值积分法，并应用于不同马赫数绕流模拟；通过对不同流域一维激波管问题、二维圆柱绕流问题和三维球体绕流的计算研究，并将计算结果与其他途径得到的研究结果诸如DSMC模拟值、N-S解及有关实验数据进行比较分析，创建了一套能有效模拟稀薄流到连续流不同流域气体流动问题简化的统一数值算法研究框架

Dichotomy, a simple iterative method Yi Newton iteration of these three methods for nonlinear equations ro...

二分法，简单迭代法矣牛顿迭代法这三种方法来求非线性的方程的根，比较这三种的收敛性。

Based on utilizing the unified chaotic model to obtain initial points of Newton iteration method, a new method for solving sets of nonlinear equations is proposed.

以统一混沌模型产生牛顿迭代的初始点，提出了基于统一混沌的牛顿迭代法求解非线性方程组的新方法。

The kinematic equations of the flow of Newtonian fluid in annulus with the inner cylinder executing a planetary motion were transformed using undetermined coefficient method, and the calculation formula of pressure gradient of the flow was obtained with the given flow rate.

利用待定系数法对牛顿流体在内管做行星运动的环空中流动的运动方程进行了变换，得到了给定流量条件下牛顿流体在内管做行星运动的环空中流动的压力梯度计算公式。

Anon-Newtonian thermal elastohydrodynamic lubric ation model is set up to analyze running-in process under heavy load.

建立了非牛顿流体热弹流润滑数学模型，对重载条件下磨合过程进行数值分析，在考虑具有粘塑性本构的非牛顿流体时，采用了高效粘度法对建立的方程进行了解算。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。