# Automatic Differentiation

(Difference between revisions)
 Revision as of 23:06, 4 April 2009 (edit) (old thread on Haskell Cafe)← Previous diff Revision as of 23:22, 4 April 2009 (edit) (undo) (short explanation of automatic differentation)Next diff → Line 1: Line 1: + '''Automatic Differentiation''' roughly means that a numerical value is equipped with a derivative part, + which is updated accordingly on every function application. + Let the number $x_0$ be equipped with the derivative $x_1$: $\langle x_0,x_1 \rangle$. + For example the sinus is defined as: + * \sin\langle x_0,x_1 \rangle = \langle \sin x_0, x_1\cdot\cos x_0\rangle + You see, that's just estimating errors as in physics. + However, it becomes more interesting for vector functions. + Implementations: Implementations:

## Revision as of 23:22, 4 April 2009

Automatic Differentiation roughly means that a numerical value is equipped with a derivative part, which is updated accordingly on every function application. Let the number x0 be equipped with the derivative x1: $\langle x_0,x_1 \rangle$. For example the sinus is defined as:

• \sin\langle x_0,x_1 \rangle = \langle \sin x_0, x_1\cdot\cos x_0\rangle

You see, that's just estimating errors as in physics. However, it becomes more interesting for vector functions.

Implementations:

## 1 Power Series

You may count arithmetic with power series also as Automatic Differentiation, since this means just working with all derivatives simultaneously.