  Diffusing a graph signal at multiple scales requires computing the action of
the exponential of several multiples of the Laplacian matrix. We tighten a
bound on the approximation error of truncated Chebyshev polynomial
approximations of the exponential, hence significantly improving a priori
estimates of the polynomial order for a prescribed error. We further exploit
properties of these approximations to factorize the computation of the action
of the diffusion operator over multiple scales, thus reducing drastically its
computational cost.
