What I have
An iterative process based on the application of a very simple function to represent a rate, with total dependence among any iteration and its predecessor (one input parameter for (n)th iteration is the output parameter from the (n-1)th iteration). Specifically,
$\qquad f(x, y, z) = x + \frac{y - x}{z + 1}$
with $x$ the modeled rate (typical value between 0 and 1), $y$ the contribution of every new record to the learning about the rate (typical value 0 or 1) and $z$ some kind of convergence/learning speed parameter (typical value any integer between 30 and 900). While $y$ and $z$ are constant, $x$ would be the result of the previous calculation.
What I want
Some kind of manipulation of the function that allows some level of independence among sequential iterations, thus allowing parallelization.
What I know (or believe to) so far:
There is extensive published literature on parallel iterative methods, but most of them are about classical methods like Map-Reduce for Machine Learning on Multicore by Chu et al.
But I'm failing to recognize which of them I could "use" to help me with my simple function.
Can someone help me pointing literature on the basics of function transformation aiming towards parallelization? Any thoughts on that matter will be very helpful.