Numerical differentiation is by far not as unstable as you seem to think. And I have a long experience in using numerical derivatives for optimization problems where you don't stop to look up symbolic derivatives applying a CAS. The function obviously was only an example. For most of the functions I have used Julia's symbolic capabilities will not be sufficient.
On Monday, January 20, 2014 9:07:02 PM UTC+1, Jason Merrill wrote: > > This implementation could certainly use some love, but finite difference > differentiation is always unstable, and the situation gets worse as you > take higher order derivatives. > > You might want to consider using the differentiate method to take your > derivatives symbolically (if this works for the functions you're using), or > have a look at the differentiation example in PowerSeries.jl. To do a > symbolic second derivative, you can do, e.g. > > julia> using Calculus > julia> @eval d2(x) = $(differentiate(differentiate(:(sin(x))))) > julia> d2(1.0) > -0.8414709848078965 > >
