["Followup-To:" header set to comp.graphics.algorithms.]
On 2007-07-11, Linus Utopia <linus_utopia@[EMAIL PROTECTED]
> wrote:
> 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
> ****tion 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)?
Um. What would be the point? You could just stop the curve when the
absolute value between the two curves diverges beyond some point.
> 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.
It seems odd (dishonest) to create an algorithm whose purpsose is to
only accept data points which lie upon the ideal curve. If you can't
discern where your experiment produces bad data and why, how can you
expect
some blind algorithm to do it for you?
> 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.
That's hardly surprising, given ordinary numeric instability.
> 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)...
Since you are already drawing the ideal curve, it hardly seems necessary
to use any data at all.
Mark
>
> Please shed some lights on me! Thanks a lot!
>
>
>
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