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Functional differentiation

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(explanation of Functional differentiation)
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There are several ways to do this:
 
There are several ways to do this:
 
* Approximate the derivative <math>f'(x)</math> by <math>\frac{f(x+h)-f(x)}{h}</math> where <math>h</math> is close to zero. (or at best the square root of the machine precision <math>\varepsilon</math>.
 
* Approximate the derivative <math>f'(x)</math> by <math>\frac{f(x+h)-f(x)}{h}</math> where <math>h</math> is close to zero. (or at best the square root of the machine precision <math>\varepsilon</math>.
* Compute the derivative of <math>f</math> symbolically. This approach is particularly interesting for Haskell.
+
* Compute the derivative of <math>f</math> [[Typeful_symbolic_differentiation|symbolically]]. This approach is particularly interesting for Haskell.
   
 
== Blog Posts ==
 
== Blog Posts ==

Revision as of 15:54, 20 June 2007

1 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.

2 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.