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InterpolatedFunction esoterica

Can anyone --- maybe somebody at WRI --- tell me how all those numbers
in an InterpolatedFunction are calculated?

For example, if

f=f /. NDSolve[{f'[t]==E^(-t^2), f[0]==0}, f, {t,0,1}][[1]]

then f is given as an interpolated function, and InputForm[f] shows the
numbers, in various lists, that Mathematica needs to calculate the
values of f.  I haven't been able to figure out what they all mean, and
I'd like to know.


Will Self

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