Fri Mar 8 13:24:40 EST 2013

Exponentials: approximation error should not introduce instability

approximation exp'(x) ~= exp(x)  s.t.  |exp'(x)| < |exp(x)|

One question that bugs me is that exp(x) = exp(x/2) * exp(x/2).

The smaller the argument of x gets, the faster the series converges.
At what point does this successive squaring get imprecise?
I.e. exp(x/2^n) might be more precise, but the squaring looses
information again.