Secant Method Calculator
Find roots of equations using the secant method (derivative-free Newton-like method).
Function f(x)
Initial Guesses
Parameters
Secant Formula
x_(n+1) = x_n - f(x_n) * (x_n - x_(n-1)) / (f(x_n) - f(x_(n-1)))
Approximates derivative using finite difference.
Root
1.4142135621
Converged in 5 iterations
f(root)
-8.9315e-10
Iterations
5
Iteration History
| n | x_(n-1) | x_n | x_(n+1) | Error |
|---|---|---|---|---|
| 1 | 1.000000 | 2.000000 | 1.333333 | 6.667e-1 |
| 2 | 2.000000 | 1.333333 | 1.400000 | 6.667e-2 |
| 3 | 1.333333 | 1.400000 | 1.414634 | 1.463e-2 |
| 4 | 1.400000 | 1.414634 | 1.414211 | 4.227e-4 |
| 5 | 1.414634 | 1.414211 | 1.414214 | 2.124e-6 |
About Secant Method
- Does not require derivative calculation
- Superlinear convergence (order ~1.618)
- Requires two initial guesses
- Faster than bisection, may fail where Newton works
- Good when derivative is hard to compute