Hi -

triggered by a discussion in sci.math I tried to explain to someone, how one could naively use interpolation to obtain a version of continuous tetration.

For simplicitiness I used U-tetration (x -> exp(x)-1)

In a second shot I made this a bit more general and - whoops - it comes out to be the matrix-method in disguise (but now with a bit more general approach). Nothing new to the experienced tetration-diggers here, but maybe still a nice exercise.

Happy christmas to all -

Gottfried

Interpolation [update 4 23.12.2007]

triggered by a discussion in sci.math I tried to explain to someone, how one could naively use interpolation to obtain a version of continuous tetration.

For simplicitiness I used U-tetration (x -> exp(x)-1)

In a second shot I made this a bit more general and - whoops - it comes out to be the matrix-method in disguise (but now with a bit more general approach). Nothing new to the experienced tetration-diggers here, but maybe still a nice exercise.

Happy christmas to all -

Gottfried

Interpolation [update 4 23.12.2007]

Gottfried Helms, Kassel