细推物理须行乐 何用浮名绊此身
 很久以前看过求平方根的这么一个方法,是用的迭代,按下面这个公式进行迭代即可求出a的平方根:
 其中X0可以随便取一个数.当Xn-Xn-1满足精度要求时,即可输出Xn作为答案.
 很长时间以来都想不明白,为什么通过这样的迭代会算出平方根.上网查他的原理也没查到.最近在"边缘奇迹 -  - 相变与临界"上看到了重正化群中类似的东西,我恍然大悟,想到了怎样来理解.
 不过,我还是不知道这个迭代式是怎么找到的,我尝试过写出求三次方根的迭代式,结果无功而返.
 上面的均属个人见解,如有错误请指出.
 8 Comments Post a comment
 这个应该是有牛顿切线法的结果吧......
 相似的,求 a 的 m 次方根的迭代式应该是:
 应该是重整化群利用了不动点的知识,而不是不动点利用重整化群的知识,你现在大几了?知道的东西真不少
 我是高三的...
 我只是看到了那本书上的一点关于重整化群的东西,对它并不清楚
 姑娘, 这个是牛顿迭代公式的变形;理解复杂化了
 我知道如果把一无理数平方根化成以1为分子的连分数,那么这个连分数的分母是循环的.进一步可以退出一个迭代公式,可以进行逐步提高精度的迭代计算.
 这就是不动点嘛
 评论里的大佬们打开了我的眼界,感恩数学,感恩简单易懂的博客!
 Note: HTML is allowed. Your email address will never be published.
 如何评价央行官员称"人民币中长期将升值,国际化条件下央行将放弃汇率目标"?
 房贷利率对房价的影响
 2021年美国买房的一些思考
 一个与直觉相悖的概率问题及其引发的严肃思考
 用人类历史理解外星人,可能有误解
 如何辨别自己在现实还是梦中
 Tags
 学而时嘻之
 宇宙的心弦
 We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. By clicking "Accept", you consent to the use of ALL the cookies.
 This website uses cookies to improve your experience while you navigate through the website. Out of these cookies, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may have an effect on your browsing experience.
 Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
 Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.