Mathematica has some excellent tools for fixed point iteration.

What I am curious about is if there is a way to have Mathematica enumerate the choice(s) for the iteration function?

For example, if we have $f(x) = x^3+4x^2-10$, we want various test functions $x = g(x)$, and we can calculate various ones from $f(x)$ as:

• $g_1(x) = x - x^3 - 4 x^2 + 10$
• $g_2(x) = \sqrt{\dfrac{10}{x} - 4 x}$
• $g_3(x) = \dfrac{1}{2} \sqrt{10 - x^3}$
• $g_4(x) = \sqrt{\dfrac{10}{4 + x}}$
• $g_5(x) = x - \dfrac{x^3 + 4 x^2 - 10}{3 x^2 + 8 x}$

It is possible there are more, we are just creating permutations of $f(x)$ by solving $x = g_i(x)$.

Is there some way to coax Mathematica to calculate all these variations?

Regards