How to interpolate this curve?
Hi all,
Please take a look at the following plot:
http://img63.imageshack.us/img63/5599/gggyf5.jpg
There are two curves:
The red one is the ideal one and the blue one is the real data from
experiments.
Due to some numerical instability, the real data strays away from the
ideal
curve at around x=15, and then begins oscillates weirdly after x=19. Since
the real data is definitely wrong beyond x=19, I only capture the real
data
from x=1 to x=19.
I also know that at x=+infinity, the asymptotic value of the curve should
be
1.5. That's to say, the ideal curve slowly converges to y=1.5 from below
and
in theory it never touches y=1.5, but numerically, it can reach y=1.5 when
x
is a very large number.
The questions is how to recover the ideal curve(the red one) from the
portion of the real data(the blue curve, up to x=19). More specifically:
1. Is there a symtematic method to detect the turning point starting from
which the real curve begins to stray away from the ideal curve (here is
x=15)?
If I throw away the data from x=15 to x=19, and only do the interpolaton
based on the data from x=1 to x=15. Then I will probably do a very good
job
fitting the curve. However, I want to find a systematic method that works
automatically and programmatically for all such curves but with varying
turning points. It's going to be troublesome if every time I have to
physically inspect the curves use my eyes manually.
2. Is there a way to utilize the knowledge of the asymptotic value y=1.5?
I tried to do polynomial fit and other cubic line fit for x=1 to 19 and
then
x=100000(at which y=1.5), but the result is not very good.
There must be a way to exploit the smoothness of the curve and recover the
ideal curve(the red one) based on the partial real data(the blue curve, up
to x=19, before it diverges)...
Please shed some lights on me! Thanks a lot!
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