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今天小编为大家带来“牛顿迭代法”，欢迎您的访问。
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increase knowledge，and leave beautiful.
Dear，this is the Learing Yard Academy!
Today，the editor brings the"牛顿迭代法”.
Welcome to visit!
思维导图
相信学过高数的友友们都接触过二分法，切线法，割线法。今天歪歪就来聊聊其中有意思的切线法吧！
切线法也叫牛顿迭代法、牛顿法，是一种迭代求解函数零点的方法。
I believe that those of you who have studied high numbers have been exposed to dichotomies, tangents and secants. Today, let's talk about the interesting tangential method.
Tangent method is also called Newton iteration method, Newton method, is a method of iteratively solving the zero of a function.
一.什么是牛顿迭代法？
牛顿迭代法（Newton's method）又称为牛顿-拉夫逊（拉弗森）方法（Newton-Raphson method），它是牛顿在17世纪提出的一种在实数域和复数域上近似求解方程的方法。
i. What is Newton iteration?
Newton's iterative method, also known as Newton-Raphson method, was proposed by Newton in the 17th century to approximate the solution of equations in the field of real numbers and complex numbers.
二.公式的推导
如图所示
ii. Derivation of formula
As shown
三.牛顿迭代法的几何意义
如图所示（适用情况）
iii. Geometric significance of Newton iteration method
As shown (applicable)
很明显，在不断使用牛顿迭代法的过程中从X0一直到Xn的过程中，我们取得点便不断趋近于实际的解。
那么什么情况下，牛顿法不适用呢，接下来我将通过举反例的方式来更全面的介绍牛顿法！
如图所示（不适用情况）
And obviously, as we go from X0 all the way to Xn using Newton's method, we're getting closer and closer to the actual solution.
So when Newton's method does not apply, next I will give a more comprehensive introduction to Newton's method by using a counter-example!
As shown (not applicable)
显然，通过不断取点，无论怎么作牛顿迭代法，我们一直都取不到近似解。所以牛顿迭代法到底怎么使用呢？接下来将从他的特点来观察和解读此方法的使用规则。
Obviously, by taking points, no matter how we do Newton's iteration, we're never going to get an approximate solution. So how does Newton iteration work? Next, we will observe and interpret the rules of using this method from its characteristics.
四.牛顿迭代法的特点
- 首先牛顿迭代法对初值X0要求极高，一般来说，牛顿迭代法只具有局部收敛性，当X0在收敛区间里内时，收敛速度极快。但相距近似解X较远时，则不建议使用此方法。
- 因为求单根时收敛速度极快的原因，所以相比于其他求近似解的方法，我们优先选择牛顿迭代法。（ps：对于求解重根的情况，此处不作要求，感兴趣的友友们，可以自行查阅资料学习。）
iv. The characteristics of Newton iteration method
First of all, Newton iteration method has extremely high requirements on the initial value X0. Generally speaking, Newton iteration method only has local convergence. When X0 is within the convergence interval, the convergence rate is extremely fast. However, it is not recommended to use this method when the approximate solution X is far away.
Compared with other methods for solving approximate solutions, Newton iteration method is preferred because of the very fast convergence speed when solving simple roots. (ps: For solving the case of heavy roots, here is not required, interested friends, you can refer to the information to learn.)
最后歪歪在这里做一下总结，牛顿迭代法不止于高数有所运用，牛顿迭代法更是一个极好的最优化算法，对编程有强烈兴趣的友友们建议去了解哦！
Finally crooked here to make a summary, Newton iterative method is not only used in high number, Newton iterative method is an excellent optimization algorithm, have a strong interest in programming friends suggest to understand oh!
今天的分享就到这里了，如果您对文章有独特的想法，欢迎给我们留言。让我们相约明天，祝您今天过得开心快乐!
That's all for today's sharing. If you have a unique idea about thearticle，please leave us a message，and let us meet tomorrow. I wish you a nice day!
参考资料：百度百科-秒懂百科、bilibili
翻译来源：有道翻译
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