10/14/2023, 11:06 PM
So we all know we can use fixed point to calculate iterations. Functions that converge to a real value, then using Schroeder's equation to compute it.
But, when the function converges to a oscillating pattern? When the upper limit and downwards limit converges, and it keeps oscillating between the 2 (like for \({^x}a\) when \(a\) is between \(0\) and \(e^{-e}\)), is there a way, an equation to compute it?
The only way I've found to do so, is with function that converge into the negative iterations and oscillates in the positive (or vice versa if you use the inverse function). You compute it on the converging side, then apply the inverse function, but it's kinda cheating...
But, when the function converges to a oscillating pattern? When the upper limit and downwards limit converges, and it keeps oscillating between the 2 (like for \({^x}a\) when \(a\) is between \(0\) and \(e^{-e}\)), is there a way, an equation to compute it?
The only way I've found to do so, is with function that converge into the negative iterations and oscillates in the positive (or vice versa if you use the inverse function). You compute it on the converging side, then apply the inverse function, but it's kinda cheating...
Regards
Shanghai46
Shanghai46