弦截法求方程根

THE SECANT METHOD

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite difference approximation of Newton's method. However, the method was developed independently of Newton's method, and predated the latter by over 3,000 years.

/*
 * =====================================================================================
 *
 *       Filename:  secant_method.cc
 *
 *    Description:  secant method
 *
 *        Version:  1.0
 *        Created:  2015年07月16日 13时53分26秒
 *       Revision:  none
 *       Compiler:  g++
 *
 *         Author:  YOUR NAME (), 
 *   Organization:  
 *
 * =====================================================================================
 */
#include <iostream>
#include <cmath>
using namespace std;

double f(double x)                              //所要求解的函数公式
{
    return x*x*x - 3*x -1;
}

double point(double a, double b)                //求解弦与x轴的交点
{
    return (a*f(b) - b*f(a))/(f(b) - f(a));
}

double root(double a, double b)                 //用弦截法求方程在[a, b]区间的根
{
    double x, y, y1;
    y1 = f(a);
    do {
        x = point(a, b);                        //求交点x坐标
        y = f(x);                               //求y
        if (y*y1 > 0)
            y1 = y, a = x;
        else
            b = x;
    }while (fabs(y) >= 0.000001);               //计算精密度
    return x;
}

int main()
{
    double a, b;
    cin>>a>>b;
    cout<<"root = "<<root(a, b)<<endl;
    return 0;
}