Thu Mar 14 18:47:03 EDT 2013
Direct computation of 2D series
These are all interesting problems, but not sure if it is useful to
solve them. There might be a simpler way to compute the 2D Taylor
series directly through differentials (autodiff).
( I'm thinking that diff is more work since there are more terms to
compute -- the tensors with partial derivatives -- but maybe the same
explosion happens for the function composition of sequences. A
serious case of bad intuition here.. )
But... for 2 variables this isn't really such an explosion, is it?
1 f_x f_y
2 f_xx f_xy f_yy
3 f_xxx f_xxy f_xyy f_yyy
Still not convinced this will work for exp((P1 - log(p0)) / N).
Somehow not explicitly using the fact that P1 - log(p0) is small seems
to be be wrong, i.e. nothing special. Somewhere, some cancelling is
going on eventually, but in what way?