Category:Newton's Method

This category contains pages concerning Newton's Method in the context of Numerical Analysis:

Newton's Method is a method of solving an equation expressed as a real function for which there may be no convenient closed form solution.

The derivative of the function has to be known in order to use Newton's Method.

Let the equation to be solved be of the form:

$y = \map f x$

Let the value of $x$ be required for a given $y$.

Let $x_1$ be an initial guess.

Then an iterative improvement on $x_1$ is of the form:

$x_2 = x_1 - \dfrac {\map f {x_1} - y} {\map {f'} {x_1} }$

where $\map {f'} {x_1}$ is the derivative of $f$ with respect to $x$ evaluated at $x_1$.