Limit Guessing Algorithm

[Paul Rubin]

"ram.rachum at gmail.com" <ram.rachum at gmail.com> writes:
> > I think I understood the question.  It sounds like a numerical methods
> > homework problem.  Basically you have f(x0), f(x1), etc. and you want
> > to extrapolate to x=infinity.  Hint: think of a0=1/x0, a1=1/x1, etc.
> > so your initial data is f(1/a0), f(1/a1), etc. and it should be pretty
> > obvious what to do next.
> 
> Well Paul, it's not obvious to me, so if you could explain it I'll be
> grateful.

Basically define g(x) = f(1/x).  So you have this g(a0), g(a1), g(a2), ...
and you can fit a curve through them with your favorite extrapolation
formula (see a numerics book for lots of choices).  Then compute g(0).