  An iterative scheme based on the kernel polynomial method is devised for the
efficient computation of the one-body density matrix of weakly interacting Bose
gases within Bogoliubov theory. This scheme is used to analyze the coherence
properties of disordered bosons in one and two dimensions. In the
one-dimensional geometry, we examine the quantum phase transition between
superfluid and Bose glass at weak interactions, and we recover the scaling of
the phase boundary that was characterized using a direct spectral approach by
Fontanesi et al. [Phys. Rev. A 81, 053603 (2010)]. The kernel polynomial scheme
is also used to study the disorder-induced condensate depletion in the
two-dimensional geometry. Our approach paves the way for an analysis of
coherence properties of Bose gases across the superfluid-insulator transition
in two and three dimensions.
