The title says it all:
What is the equation for the error of the Newton-Raphson method?
Also... an explanation for each of the terms would be nice... I'm a comp sci guy, not typically a math guy.
The title says it all:
What is the equation for the error of the Newton-Raphson method?
Also... an explanation for each of the terms would be nice... I'm a comp sci guy, not typically a math guy.
Suppose you're using Newton-Raphson to solve $f(x)=0$ where $f$ is a twice differentiable function, so x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}, and $f(r) = 0$. Then r - x_{n+1} = - \frac{f''(c) (r - x_n)^2}{2 f'(x_n)} where $c$ is some point between $r$ and $x_n$. If f'' is continuous, f'(r) \ne 0 and $x_n$ is close to $r$, f''(c)/f'(x_n) will be close to f''(r)/f'(r), so this says the error in $x_{n+1}$ is approximately a constant times the square of the error in $x_n$.