Rescue Me!!!!

[newton123]

I am writing a program that solves for the root of a polynomial using newton raphson method.Newton-Raphson has the following algorithm:

• Make one initial guess, x0
• Repeat the following step to get a new
guess, x[k+1], from the old guess, x[k]
-Compute x[k+1] from the following equation

x[k+1] = x[k] - f(x[k])/f'(x[k])
• Continue iteration until the value of x[k+1]
and/or f(x[k+1]) is sufficiently accurate

If you try it with this polynomial: x^2 - 5x + 2 with initial guess of 4 at 3rd iteration you should get a root of 4.561553..

My code below runs but don't give correct results.. Please help me .. Thank you so much.

Here is the sample using the function above:

Enter the power of the equation: 2
Enter the coefficient of x^2: 1
Enter the coefficient of x^1: -5
Enter the constant term: 2

Enter a guess: 4
Set maximum number of iteration: 3

4
1.#INF00000000
-1.#IND0000000
-1.#IND0000000

The approximate root is -1.#IND0000000

This answer is very far from reality.

  #include <iostream>
#include <math.h>
using namespace std;

const int MAX = 1000;
int p;
double f(double);
double df(double);
double coeff[MAX], dcoeff[MAX];
double newtonraphson(double);

int main()
{
    double x[MAX];
    int imax, icount, i;
    double guess, tol;
    
    
     //Get Function
 cout << "Enter the power of the equation: ";
 cin >> p;
   
 for(int i = p; i > 0; i--)
 { 
   cout << "Enter the coefficient of x^" << i << ": ";
   cin >> coeff[i];
 }
 cout << "Enter the constant term: ";
 cin >> coeff[0];
 cout << endl;
 
 //Final inputs
   
   cout << "Enter a guess: ";
    cin >> x[0];
    

    cout << "Set maximum number of iteration: ";
    cin >> imax;
    
    x[1] = newtonraphson(x[0]);
    
    for(i = 1; i < imax; i++)
    {
        x[i+1] = newtonraphson(x[i]);     
            
    }
    
    //outputs the approximate root
    
    cout << x[0] << endl;
    
    for(i = 0; i < imax; i++)
    {
            cout.setf(ios::fixed);
            cout.setf(ios::showpoint);
            cout.precision(20);
            cout << x[i+1] << endl;
    }
    
    cout << "The approximate root is: ";
    cout << x[imax-1];
    
    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 df(double x)
{
       int i;
       double val = 0;
        for(i = 0; i < p; i++)
        {
              val += (dcoeff[i] * pow(x, i));
        }
            return val;
}
double newtonraphson(double xo)
{
      return xo - f(xo)/df(xo);
}

[kevinkjt2000]

I do not see where in the program that dcoeff is filled?

[newton123]

i was thinking maybe i need another array for the first derivative .. i chaged that to coeff[i], i'm still getting the same error..

[kevinkjt2000]

You should probably have a derivative be calculated using the power rule.
For example d/dx(4x^3 - 5x + 2) = 12x^2 - 5