11/03/2007, 09:08 PM
re a)
I would stay with the established notation, i.e. use
\( \exp_b^{\circ n}(x) \) or \( \exp_b^{[n]}(x) \)
instead of \( \{b,x\}^n \).
re b)
It was not clear what function \( f(b,x_0) \) do you want to use, I would guess \( f(b,x_0)=b^{x_0} \). It is also not clear whether this average method converges. All fixed points of \( b^x \) are repelling except the lower real fixed point (if existing).
re c)
Didnt get the Euler summation for diverging newton method ...
I would stay with the established notation, i.e. use
\( \exp_b^{\circ n}(x) \) or \( \exp_b^{[n]}(x) \)
instead of \( \{b,x\}^n \).
re b)
It was not clear what function \( f(b,x_0) \) do you want to use, I would guess \( f(b,x_0)=b^{x_0} \). It is also not clear whether this average method converges. All fixed points of \( b^x \) are repelling except the lower real fixed point (if existing).
re c)
Didnt get the Euler summation for diverging newton method ...