I'm trying to obtain an interpolation function for points of an x^(-5) function (which goes to infinity at x = 0).
hyper = Flatten[Table[[x^(-5)], {x, 1, 100}]];
points = Range[100];
data = Transpose@{points, hyper}
If I do a ListPlot of data, I have:
If I use interpolation like:
Interpolation[data, Method -> "Spline"]
Interpolation[data, Method -> "Hermite"]
I get an interpolating function with this form:
Clearly, the interpolation function has not the simplest form for 'joining' those points, since it has an uprising between x = 3 and x = 4, and an oscillatory behavior.
My question is: Can I make some kind of interpolation to data which reproduces the form of the true function, without those oscillations?
In particular, I'm interested in get an appropriate value of the interpolating function at x = 3.68, for example.
Thanks for the answers.
Interpolation[data, InterpolationOrder -> 2]
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