  The past thirteen years have seen the development of many algorithms for
approximating matrix functions in O(N) time, where N is the basis size. These
O(N) algorithms rely on assumptions about the spatial locality of the matrix
function; therefore their validity depends very much on the argument of the
matrix function. In this article I carefully examine the validity of certain
O(N) algorithms when applied to hamiltonians of disordered systems. I focus on
the prototypical disordered system, the Anderson model. I find that O(N)
algorithms for the density matrix function can be used well below the Anderson
transition (i.e. in the metallic phase;) they fail only when the coherence
length becomes large. This paper also includes some experimental results about
the Anderson model's behavior across a range of disorders.
