In this paper, we propose efficient numerical techniques for Butterworth filtering and implicit fairing of large irregular triangle meshes, where the corresponding filters are rational polynomials and the resulting large linear systems need to be solved iteratively. We show that significant speed-up can be achieved for Butterworth filtering by factorizing the linear system in the complex domain. As for implicit fairing, with our estimate of the optimal extrapolation parameter ω, successive overrelaxation (SOR) offers great improvements, both in speed and space usage, over the more familiar conjugate gradient type solvers.