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#include <iostream>
#include <math.h>
#include <iomanip>
using namespace std;
int p, maxi = 1000;
const int MAX = 1000;
double coeff[MAX], dcoeff[MAX];
double xplus, xminus;
double f(double);
double bisection(double, double);
double falsi(double, double);
double df(double);
double ddf(double);
int main()
{
int method, out, selection;
double guess1, guess2, value1, value2, etol;
double xnew[MAX], xplus[MAX], xminus[MAX];
int imax;
double x[MAX];
//Get Function
cout << "\tEnter the order of the equation: ";
cin >> p;
for(int i = p; i > 0; i--)
{
cout << "\tEnter the coefficient of x^" << i << ": ";
cin >> coeff[i];
}
cout << "\tEnter the constant term: ";
cin >> coeff[0];
cout << endl;
//Sign Change
do
{
cout << "\tEnter first initial guess: ";
cin >> guess1;
cout << "\tEnter second initial guess: ";
cin >> guess2;
value1 = f(guess1);
value2 = f(guess2);
if(value1 * value2 < 0)
{
cout << endl;
cout << "\tA root has been bracketed!";
cout << endl << endl;
}
else
{
cout << endl << endl;
cout << "\tNo root is bracketed! "
<< "Increase delta x or find another guess!";
cout << endl << endl;
}
}while(!((value1 * value2) < 0));
//Assigning xplus and xminus
if(value1 > 0)
{
xplus[0] = guess1;
xminus[0] = guess2;
}
else
{
xplus[0] = guess2;
xminus[0] = guess1;
}
//Final inputs
cout << "\tInitial guess which gives f(x) > 0 is : " << xplus[0];
cout << endl;
cout << "\tInitial guess which gives f(x) < 0 is : " << xminus[0];
cout << endl << endl;
cout << "\tSet maximum number of iterations: ";
cin >> imax;
//The Heart of Bisection Method
for(int i = 0; i < imax; i++)
{
xnew[i] = bisection(xplus[i], xminus[i]);
if(f(xnew[i])> 0)
{
xplus[i+1] = xnew[i];
xminus[i+1]=xminus[i];
}
else
{
xminus[i+1] = xnew[i];
xplus[i+1]=xplus[i];
}
}
//For Good Output.
cout << endl << endl;
cout << "\t___________________________________________________________________________________"<< endl;
cout << "\tIteration x+ x- f(x+) f(x-) midpoint error " << endl;
cout << "\t___________________________________________________________________________________" << endl;
for(int i = 0; i < imax; i++)
{
cout <<"\t" << setw(5) << i+1 << ' '
<< setw(10) << xplus[i] << ' '
<< setw(11) << xminus[i] << ' '
<< setw(12) << f(xplus[i]) << ' '
<< setw(12) << f(xminus[i]) << ' '
<< setw(10) << xnew[i] << ' '
<< setw(10) << xplus[i] - xminus[i] << ' '
<< endl;
}
cout << "\t_____________________________________________________________________________________"<< endl;
cout << endl << endl << endl;
cout << "\tThe root is approximately: ";
cout.setf(ios::fixed);
cout.setf(ios::showpoint);
cout.precision(20);
cout << "\t" << xnew[imax-1];
cout << "\n\tWith error of: " <<"\t\t\t" << xplus[imax] - xminus[imax];
cin.get();
cin.get();
return 0;
}
double f(double x)
{
int i;
double s = 0;
for(i = 0; i <= p; i++)
{
s += coeff[i] * pow(x, i);
}
return s;
}
double bisection(double xp, double xm)
{
return (xp + xm) * .5;
}
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