Newton-Raphson Calculator
Find roots of equations using the Newton-Raphson iterative method.
Function f(x)
Parameters
Newton-Raphson Formula
x_(n+1) = x_n - f(x_n) / f'(x_n)
Root
1.4142135624
Converged in 4 iterations
f(root)
4.5106e-12
Iterations
4
Iteration History
| n | x_n | f(x_n) | Error |
|---|---|---|---|
| 1 | 2.00000000 | 2.000e+0 | 5.000e-1 |
| 2 | 1.50000000 | 2.500e-1 | 8.333e-2 |
| 3 | 1.41666667 | 6.944e-3 | 2.451e-3 |
| 4 | 1.41421569 | 6.007e-6 | 2.124e-6 |
About Newton-Raphson
- Quadratic convergence near simple roots
- Requires derivative of function
- May diverge if initial guess is poor
- Fails when derivative is zero