(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 also converge to the self-root on .

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 which is positive everywhere.

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.