Contraction

https://en.wikipedia.org/wiki/Contraction_(operator_theory)

$\gamma$-Contraction

An update operation is a $\gamma$-contraction in max-norm if and only if for all $U_i,V_i$: $\Vert U_{i+1}-V_{i+1}\Vert \le \gamma \Vert U_i-V_i\Vert$

Theorem: A contraction converges to a unique fixed point, no matter initialization.