Category:Halley's Method

This category contains pages concerning Halley's Method:

Halley's Method is a method of solving an equation $\map f x = 0$ involving the real function $f$ for which there may be no convenient closed form solution.

The derivative and the second derivative of $f$ have to be known in order to use Halley's Method.

Let $x_0$ be an initial guess.

Halley's Method uses the iteration:

$x_{n + 1} = x_n - \dfrac {\map f {x_n} } {\map {f'} {x_n} - \dfrac {\map f {x_n} \map {f} {x_n} } {2 \map {f'} {x_n} } }$

where:

$\map {f'} {x_n}$ is the derivative of $f$ with respect to $x$ evaluated at $x_n$

$\map {f} {x_n}$ is the second derivative of $f$ with respect to $x$ evaluated at $x_n$.