Definition:Secant Method

Definition

Let $f: \R \to \R$ be a real function which has a root which is to be found.

The secant method is an iterative technique for achieving this, by setting up the following iterative function:

$x_{n + 1} = x_n - \dfrac {\map f {x_n} \paren {x_n - x_{n - 1} } } {\map f {x_n} - \map f {x_{n - 1} } }$ for $n = 1, 2, 3, \ldots$

where $x_0$ and $x_1$ are first approximations to the root.

Convergence is not guaranteed.

Also see

• Definition:Newton-Raphson Method

• Results about the secant method can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): secant method
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): secant method