Talk:Automatic differentiation

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What is the connection between Automatic Differentiation and Dual Numbers?

Well, I would say that if P is a polynomial, and ε2 = 0 in the usual way of the dual numbers, then
P(a + ε) = P(a) +P′(a)ε

is an identity in the dual numbers that expresses 'automatic differentiation'.

Charles Matthews 15:57, 12 Jul 2004 (UTC)


I believe the article should be changed so that the mathematics is separated from the use of the mathematical idea in computer programs. Somwthing like this: First the pure mathematical stuff, then some stuff about the fact that automatic differentiation can either be implemented by operator overloading, wich is nice if you want to do numerical differentiation. Or it can be implemented by automatically transforming a program to calculate the derivatives of functions when they are called, which is nice if you need derivatives of functions but don't bother to edit the source code. Comments? --DanielJanzon 16:14, 8 October 2005 (UTC)

I agree that it's generally a good idea to separate the maths from the implementation. Your comment implies that this isn't done in the current article; however, it seems to me that the implementation is not mentioned at all. Anyway, please go ahead and describe the implementation techniques you mentioned (operator overloading and transforming the source code). -- Jitse Niesen (talk) 17:11, 8 October 2005 (UTC)