What are some functions that gives vastly different results when interpolated with spline, in comparison to linear or to polynomial interpolation? For example i tried with sigmoid and bump function, both gives almost same results, no matter which interpolating method i use
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I had some problem interpolating $\ln(-\ln x)$ with polynomials for $\int\limits_0^1\ln(-\ln x),dx$, maybe you can try something on this one? – Alexey Burdin Nov 21 '19 at 22:12
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this function that takes domain [0:1] and rest is undefined? – computerscientist Nov 21 '19 at 22:24
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For real-valued $\log$ and $x\in \mathbb{R}$ I think yes: for $\ln(-\ln(x))$ to be real we need $-\ln(x)>0$ so $\ln(x)<0$, so $x<1$, but $x>0$ for the inner $\ln$ to be real. Thus $0<x<1$. – Alexey Burdin Nov 21 '19 at 22:31
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i tried with function sugested above: $$ f(x) = ln(-ln(x)) $$ But there is not much difference between interpolation methods,as you can see there is only difference and the ends of domain. gnuplot comparison of interpolation methods
Arent there any functions that have more visible difference?
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I think you should update the question though rather than posting this as an answer, sorry. The plot differs rather much for $x\in[0.8,1)$ on the picture. What order of polynomials did you use? I tried 61th, but couldn't get enough accuracy though. – Alexey Burdin Nov 21 '19 at 23:32