There is another method to calculate any order derivatives, very similar to this one, known as Multi-complex differentiation. This method can calculate derivatives up-to any order.
http://www.autodiff.org/Docs/euroad/13rd%20EuroAd%20Workshop%20-%20Thierry%20Dargent%20-%20Using%20Multicomplex%20Variables%20for%20Automatic%20Computation%20of%20High-Order%20Derivatives.pdf http://delivery.acm.org/10.1145/2170000/2168774/a16-lantoine.pdf?ip=207.151.221.1&id=2168774&acc=ACTIVE%20SERVICE&key=6405B83BDA580DC2%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35&CFID=717380051&CFTOKEN=25446753&__acm__=1443489222_ee3f3d4c7ee41030aaba536e14d6a6ab I have used this in my field and it seems to work nicely. thanks, Nitin On Saturday, March 29, 2014 at 5:43:05 PM UTC-7, Rob J Goedman wrote: > > Hi, > > As a first 'jump into the fray' exercise I've attempted to translate > Jeffrey Fike's hyper-dual numbers code from c++ to Julia, more or less > following the DualNumbers package. > > The c++ code can be found at http://adl.stanford.edu/hyperdual/hyperdual.h > . The paper itself at > http://adl.stanford.edu/hyperdual/Fike_AIAA-2011-886.pdf . > > The Julia package can be found at: > https://github.com/goedman/HyperDualNumbers.jl.git . > > Of course, I'm pretty new at this so I'm sure there will be errors and > poor practices. So any feedback is appreciated. > > Also, I'm wondering if the type should be called Hyper or a better name > would be HyperDual. > > This work was triggered by the interesting threads around openPP, > TaylorSeries.jl, Calculus2, PowerSeries.jl (and at some time I hope > MCMC.jl). > > Rob J. Goedman > goe...@icloud.com <javascript:> > > > > >
