算法之【牛顿迭代法】

众所周知，计算机的基本数值算法是加减乘除，甚至只是加减法。而次方和开根算法都是由四则运算混合表示而成的，因而根号计算比四则运算要慢很多。无理数如√2的浮点数计算就是由牛顿迭代法得出的。牛顿迭代法是一种用于计算曲线方程根的精确算法（尤其是幂函数方程），比二分法更加高效，因为它基于微分。

As we all know, basic numerical calculation in the computer is: addition, subtraction, multiplication and division.

Or even only the addition and subtraction. But the power and root algorithm is a complex combination of the four fundamental operations, so they are much slower. Irrational numbers such as √2 whose floating point is obtained by the Newton-Raphson method. Newton-Raphson method is a precise algorithm used to calculate the curvilinear equation (especiallypower function), it’s more efficient than Dichotomy because it is based on the differential.

以计算√x（精度e）为例的c语言函数：

A example using C language calculating √x with precision ’e’:

double abs_value(double x)

{

 if(x<0)x=-x;

 return x;

}

double sqrt_root(double x,double e)

{

 double x0=1;

 while(abs_value(x0*x0-x)>e)

X0=(x0+x/x0)/2;

 return x0;

}