  We derive an improved version of the recursive Green's function formalism
(RGF), which is a standard tool in the quantum transport theory. We consider
the case of disordered quasi one-dimensional materials where the disorder is
applied in form of randomly distributed realistic defects, leading to partly
periodic Hamiltonian matrices. The algorithm accelerates the common RGF in the
recursive decimation scheme, using the iteration steps of the renormalization
decimation algorithm. This leads to a smaller effective system, which is
treated using the common forward iteration scheme. The computational complexity
scales linearly with the number of defects, instead of linearly with the total
system length for the conventional approach. We show that the scaling of the
calculation time of the Green's function depends on the defect density of a
random test system. Furthermore, we discuss the calculation time and the memory
requirement of the whole transport formalism applied to defective carbon
nanotubes.
