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Re: Which interpolation?
Posted:
Dec 10, 2012 12:22 PM
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Cristiano <cristiapi@NSgmail.com> writes:
>On 07/12/2012 21:48, Dave Dodson wrote:
>> The data presented suggest that the function has a horizontal asymptote at y = 1.
>
>You're right.
>
>> If you expect that this is the case, you should try a model that has such an asymptote. E.g., y(x) = 1 + a/x + b/x^2 + ... or y(x) = A*exp(-a*x) + B*exp(-b*x) + ....
>
>I use a function similar to the former:
>y(x)= a + b / sqrt(x) + (c + (d + e / x) / x) / x
>but the question is: should I use that function (which doesn't pass over
>the calculated points and the point-to-point error is much bigger than
>the confidence interval 2.5e-6 used in the simulation) or should I use a
>spline?
>
>I'm asking that because I calculated the points using a narrow
>confidence interval, so the risk to miss the true y value should be
>small (obviously I don't know anything about the true y value).
>
>Cristiano
>
using _one_ model for the whole range and requiring such a precision
(quasi an interpolation, as you asked) will hardly fit together.
Make a plot of your discrete data, e.g. gnuplot allows you to use splines
for this,
and decide where to cut the ranges. e.g. convex monotonic , concave monotonic,
asymptotic range. when use piecewise interpolating splines which preserve
these properties and in the asymptotic range a smoothing spline.
also a possible choice would be a spline under tension which
interpolates the data and nevertheless can simultaneously model monotonicity
convexity, concavity. for the tension parameter a bit experimentation
is necessary. If the data are not too much , you can try it here
http://numawww.mathematik.tu-darmstadt.de:80
in the section interpolation/approximation
hth
peter
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