Bisect2.cpp

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//      Bisect2.cpp
 
//      Recursive function
//                      Example: Find the solution by bisection
 
//      Version 2: f(x) is globally declared and defined
//                 epsilon as global constant
 
#include <cmath>
#include <iostream>
using namespace std;
 
const double EPS = 1e-6;                // global constant
 
double f(const double x)                // declaration and
{
    return  sin(x) - 0.5 * x ;    //   definition of function f(x)
}
 
double Bisect2(const double a, const double b); // declaration of Bisect2
 
int main()
{
    double a, b;
 
    cout << endl;
    cout << "  Determine point of zero in [a,b] by bisection" << endl;
 
    cout << " f(a) > 0,  a : ";
    cin >> a;
    cout << " f(b) < 0,  b : ";
    cin >> b;
 
    double x0 = Bisect2(a, b);                  // call recursive function
 
    cout << endl;
    cout << " point of zero = " << x0 << endl;
    cout << endl;
 
    return 0;
}
 
//      ---------------------------------------------------------------
//      Recursive  function Bisect2
//      ---------------------------------------------------------------
 
double Bisect2(const double a, const double b)  // definition of Bisect2
{
    double x0, fc, c = (a + b) / 2;
 
    fc = f(c);
    if ( std::abs(fc) < EPS ) {
        x0 = c;                 // end of recursion
    }
    else if (  fc > 0.0 ) {
        x0 = Bisect2(c, b);             // search in right intervall
    }
    else {                      // i.e., fc < 0.0
        x0 = Bisect2(a, c);             // search in left intervall
    }
 
    return x0;                  // return with solution
}