I am currently trying to understand some code and am struggling with the mathematics.
In the code this function is used:
$r(\theta) = \theta +k_0 \theta^3 +k_1 \theta^5 +k_2 \theta^7 +k_3 \theta^9)$
It is also necessary to use the inverse of this function to determine a $\theta_s$ with $r(\theta_s)$ known. For this the following formula is used:
$ \theta_{n+1}=r_0/(1 +k_0 \theta_n^2 +k_1 \theta_n^4 +k_2 \theta_n^6 +k_3 \theta_n^8)$
With $\theta_0=r(\theta_s)$
In the code $ \theta_{10}$ is calculated and used.
My guess is this is some numerical approach, but every search I did returned nothing relevant.
Can anyone point me to a proof that this converges ? Alternatively what do I have to look for to understand this ?
