Functional differentiation

Introduction

Functional differentiation means computing or approximating the deriviative of a function. There are several ways to do this:

• Approximate the derivative $f'(x)$ by ${\frac {f(x+h)-f(x)}{h}}$ where $h$ is close to zero. (or at best the square root of the machine precision $\varepsilon$.
• Compute the derivative of $f$ symbolically. This approach is particularly interesting for Haskell.

Blog Posts

There have been several blog posts on this recently. I think we should gather the information together and make a nice wiki article on it here. For now, here are links to articles on the topic.

• Overloading Haskell numbers, part 2, Forward Automatic Differentiation.
• Non-standard analysis, automatic differentiation, Haskell, and other stories.
• Automatic Differentiation