  This paper proposes new factorizations for computing the Neumann series. The
factorizations are based on fast algorithms for small prime sizes series and
the splitting of large sizes into several smaller ones. We propose a different
basis for factorizations other than the well-known binary and ternary basis. We
show that is possible to reduce the overall complexity for the usual binary
decomposition from 2log2(N)-2 multiplications to around 1.72log2(N)-2 using a
basis of size five. Merging different basis we can demonstrate that we can
build fast algorithms for particular sizes. We also show the asymptotic case
where one can reduce the number of multiplications to around 1.70log2(N)-2.
Simulations are performed for applications in the context of wireless
communications and image rendering, where is necessary perform large sized
matrices inversion.
