【C】牛顿方法求函数在某点附近的零点

原理：

                       

例如：用牛顿法求下面方程在1.5附近的根：

              2*x^3 - 4*x^2 + 3*x -6 = 0

故有：f(x) = 2*x^3 - 4*x^2 + 3*x - 6

        df/dx = 6*x^2 - 8*x + 3

        x := x - f(x)/(df/dx);

C代码实现：

#include <stdio.h>
#include <math.h>


/*****************************************NEWTON'S METHODS FOR GETTING THE ROOT OF A FUNCTION*********************************************************/

/*function f(x)*/
double f(double x)
{
    return 2*pow(x,3) - 4*pow(x,2) + 3*x - 6;
}
/*function df/dx that is f'(x) */
double df(double x)
{
    return 6*x*x - 8*x + 3;
}

/*theta is the parameter of function f, and the parameter of function df*/
double Newton( double theta,double (*f)(double), double (*df)(double), const double precision )
{
    
    double x1 = (*f)(theta);
    double x2;
    do{
        x2 = x1 - (*f)(x1)/(*df)(x1);
    }while( fabs(x2-x1) < precision ? 0: (x1 = x2));
    return x2;
}

int main()
{
    double (*pf)(double) = f;
    double (*pdf)(double) = df;
    /*test*/
    printf("%lf",Newton(1.5,pf,pdf,0.0001));
    return 0;
}