Recently, Kim and Jung reported on the efficiency of certain density matrix purification polynomials for calculation of the one-particle density matrix. In this comment, it is shown that a different conclusion is reached if a more efficient method is used for polynomial evaluation. The impact of the choice of purification polynomial on sparsity and memory usage is also discussed. We comment on how the use of non-monotonic polynomials can make the convergence even faster. (C) 2012 Elsevier B. V. All rights reserved.