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Well, it's exact until you evaluate it at a float — because it's the floats that are inexact, not the technique. And that limitation is just as true of symboli
by waqf 13y ago
Well, it's exact until you evaluate it at a float — because it's the floats that are inexact, not the technique.
And that limitation is just as true of symbolic algebra. Symbolic algebra is "exact" iff you can do exact evaluation, or if your application doesn't require you to evaluate at all. Automatic differentiation is the same, it's just that the unevaluated forms in symbolic algebra are "nicer".
- deleted 13y ago[deleted]
- porges 13y ago>Dual numbers cannot, because they use plain old floating point math in the derivative equations. There's nothing stopping you from switching out the floating point for rationals or something like that. For example, the Haskell `ad` package has its functions parameterized over all instances of Num: http://hackage.haskell.org/package/ad-3.4/docs/Numeric-AD.html#v:diff http://hackage.haskell.org/package/ad-3.4/docs/Numeric-AD.ht...