#include <iostream> #include <cmath> using namespace std; void bisection(double, double, double, int); double f(double); int main() { int imax; // maximum number of iterations double a, b; // left and right ends of the original interval double epsilon; // convergence criterion // obtain the input data cout << "Enter the limits of the original search interval, a and b: "; cin >> a >> b; cout << "Enter the convergence criteria: "; cin >> epsilon; cout << "Enter the maximum number of iterations allowed: "; cin >> imax; bisection(a, b, epsilon, imax); return 0; } // A bisection function that finds roots of a function // The interval a < x < b is known to contain a root of f(x). The estimate // of the root is successively improved by finding in which half of the interval // the root lies and then replacing the original interval by that half-interval. // void bisection(double a, double b, double epsilon, int imax) { int i; // current iteration counter double x1, x2, x3; // left, right, and midpoint of current interval double f1, f2, f3; // function evaluated at these points double width; // width of original interval = (b - a) double curwidth; // width of current interval = (x3 - x1) // echo back the passed input data cout << "\nThe original search interval is from " << a << " to " << b << endl; cout << "The convergence criterion is: interval < " << epsilon << endl; cout << "The maximum number of iterations allowed is " << imax << endl; // calculate the root x1 = a; x3 = b; f1 = f(x1); f3 = f(x3); width = (b - a); // verify there is a root in the interval if (f1 * f3 > 0.0) cout << "\nNo root in the original interval exists" << endl; else { for (i = 1; i <= imax; i++) { // find which half of the interval contains the root x2 = (x1 + x3) / 2.0; f2 = f(x2); if (f1 * f2 <= 0.0) // root is in left half interval { curwidth = (x2 - x1) / 2.0; f3 = f2; x3 = x2; } else // root is in right half interval { curwidth = (x3 - x2) / 2.0; f1 = f2; x1 = x2; } if (curwidth < epsilon) { cout << "\nA root at x = " << x2 << " was found " << "in " << i << " iterations" << endl; cout << "The value of the function is " << f2 << endl; return; } } } cout << "\nAfter " << imax << " iterations, no root was found " << "within the convergence criterion" << endl; return; } // function to evaluate f(x) double f(double x) { const double PI = 3.14; return (exp(-x) - sin(0.5 * PI * x)); }