算法之【牛頓疊代法】As we all know, basic numerical calculation in the computer is: addition, subtraction, multiplication and division.

衆所周知，計算機的基本數值算法是加減乘除，甚至隻是加減法。而次方和開根算法都是由四則運算混合表示而成的，因而根号計算比四則運算要慢很多。無理數如√2的浮點數計算就是由牛頓疊代法得出的。牛頓疊代法是一種用于計算曲線方程根的精确算法（尤其是幂函數方程），比二分法更加高效，因為它基于微分。

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.

以計算√x（精度e）為例的c語言函數：

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;