Is there some standard way to approximate a complex linear homogenous recurrence with constant coefficients with a simple one?
For example, I might want to approximate
$ a_{n+k}=a_{n+k-1}+a_{n+k-2}+...+a_n $
with a geometric series
$ b_{n+1}=qb_n $
using some standard method.
I'd like to estimate the series when the root of the characteristic equation is difficult to find or doesn't have an analytic solution.