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Re: Which interpolation?
Posted:
Dec 10, 2012 12:22 PM


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 pointtopoint error is much bigger than >the confidence interval 2.5e6 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.tudarmstadt.de:80 in the section interpolation/approximation hth peter



