The most difficult part for using this theorem is to determine
. For algebraic equations it is easy to determine a value
, that we will call the order of Rouche theorem, such that
and consequently may be
obtained by computing
For non algebraic finding requires an analysis of the system.
Rouche theorem may be more efficient than Moore or Kantorovitvh theorems. For example when combined with a polynomial deflation (see section 5.9.6) it allows one to solve Wilkinson polynomial of order up to 18 with the C++ arithmetic on a PC, while stand solving procedure fails for order 13.