From: Roland Schwarz (roland.schwarz_at_[hidden])
Date: 2006-03-25 11:43:20
Roland Schwarz wrote:
> But complex of course could also turn out to be handy at times.
Too fast again (._.)
A complex function AFAIK is indefinitely differentiable by definition.
So it obviously belongs to the class of C2 but is there such a thing as
complex valued splines?
Then what about function composition? For the equivalence of complex
differentiation rules with real valued ones you need that the complex
function is identical to its real valued counterpart when evaluated on a
part of the real line (sloppy speaking). So this will force the function
class to be C_infinite. Or am I missing something?
I think c2_functions are not so much interesting because they are
carrying their derivatives with them, but because they are a handsome
tool to deal with splines in a very readable manner.
Having said this, I think c2_functions should not be used for hiding the
algorithm developers laziness to modify his/her algorithm to make use of
whatever is known about the functions (in case of analytic funtions you
know all derivatives!).
c2_functions in my opinion is a want-to-have tool to deal with splines
numerically, while still focusing on it's appearance as a function.
Other directions deviate from numerical use and extend to symbolic
systems. This would also be desirable to have, but I think it should go
to a different library.
Just what I think...
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