Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
The secant method is an iterative technique for finding the roots of a function by approximating the derivative. It uses two initial approximations to generate a sequence converging to the root.
5 Must Know Facts For Your Next Test
The secant method does not require the calculation of the derivative, unlike Newton's Method.
It uses the formula $x_{n+1} = x_n - f(x_n) \frac{x_n - x_{n-1}}{f(x_n) - f(x_{n-1})}$ to find successive approximations of the root.
Convergence of the secant method is generally slower than that of Newton's Method but faster than simple iteration methods.
The method can fail if $f(x_n)$ is equal to $f(x_{n-1})$, causing division by zero.
Choosing initial guesses that are close to the actual root improves convergence speed and accuracy.
Review Questions
Related terms
Newton's Method: An iterative technique for finding roots of a function using tangent lines, requiring computation of derivatives. The update formula is $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$.
Root-Finding Algorithm: Any algorithm used to find solutions (roots) where a function equals zero.
Derivative: A measure of how a function changes as its input changes; it represents an instantaneous rate of change.