(04/11/2009, 09:16 AM)andydude Wrote: If we interpolate these points, one would except the interpolation to diverge for infinite pentation, and x-superroot-x, but the interpolating polynomial of these integer points do seem to converge,
Now I doubt about the interpolation method.
If the interpolation of the self-tetra-root would yield a valid function,
then shoud the interpolation of the simple self-root
But this seems not to be the case.
An interpolation polynomial of degree 400 (401 sample points) still has a negative value at 0.25.
And if we compare the values it seems that the negativity gets rather worse:
101 points:
201 points:
301 points:
401 points:
So it really looks as if the interpolation (even if it converges) does not converge to
So I would conclude that the interpolation of the self-tetra-root also does not converge to a self-tetra-root, even if it converges.