02/06/2009, 06:02 PM
tommy1729 Wrote:note that this can also be used to compute
f(f(f(x))) = exp(x).
But slowly, slowly. Before we continue we first have to see whether your idea works. Thats not really clear. The thing is that the regular iteration at a fixed point depends strongly on the derivatives at the fixed point. However your function \( \exp(-x^2) \) messes up the derivations of \( \exp \) at 0. From that point of view its doubtful whether it results in something usable.
However a first step to assure the substance of the idea would be to plot the approximations of \( \exp^{1/2} \) and to see whether they really converge and if to what function \( f \) and whether this function really satisfies \( f(f(x))=\exp(x) \) (these are all open questions until now). Maybe I can do this, but not immediately. Any volunteer out there?