Fri Mar 15 10:23:26 EDT 2013
Exponentials: final word
The update data dependencies are:
(P0, P1, p0, N) -> (q01, p1)
The approximation error is:
exp(P1) - p1 = e
which could also be expressed relative to p1 if it makes sense for
e = e' p1
Because q01 is fairly precise, it should be possible to do one of these:
- ignore the drift, solve it at a higher level
- hard-reset the drift once by computing exp(P1) using more terms
- adding 1-st order compensation for q01 drift in q12 in terms of e.
Any other approach explored in the previous entries seems to loose
precision due to the inability to express that e is small. I.e. we
don't get a series expansion in e, but in P1, p1, which is not helpful.
So, time to stop analysis paralysis: it's really a non-issue. Either
find an approach that gives an expansion in e, or shut up and see what
happens in practice.