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Newton-Raphson Root Finding Method
Algorithm:
xi+1 = xi - f(xi)/f'(xi)
Example: find the roots of f(x) = 2x2 -x -21
% cat newt2.cpp
// Newton-Raphson method for finding the
// roots of f(x) = 0 for a polynomial function
#include <iostream>
using namespace std;
#include <cmath>
int main()
{
double a, b, c, x1, x0, crit, delta;
int iters = 0;
cout << "Enter values for a, b, and c :";
cin >> a >> b >> c;
cout << "Enter a guess for the root :";
cin >> x0;
cout << "Enter the convergence criterion: ";
cin >> crit;
// use a do-while loop
do
{
x1 = x0 - (a*x0*x0 + b*x0 + c) / ( 2*a*x0 + b);
delta = fabs ( x1 - x0 );
x0 = x1; // new approximation becomes the
old
// approximation for the next iteration
iters++; // count the number of iterations
} while (delta > crit && iters <= 100);
cout << "One root is " << x1 << endl;
cout << "Found in " << iters
<< " iterations" << endl;
return 0;
}
% g++ newt2.cpp
% a.out
Enter values for a, b, and c :2 -1 -21
Enter a guess for the root :9
Enter the convergence criterion: .00001
One root is 3.5
Found in 6 iterations
cswanson@mega (~/spring06) % a.out
Enter values for a, b, and c :2 -1 -21
Enter a guess for the root :-10
Enter the convergence criterion: .00001
One root is -3
Found in 6 iterations
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