  This work presents a new algorithm for matrix power series which is
near-sparse, that is, there are a large number of near-zero elements in it. The
proposed algorithm uses a filtering technique to improve the sparsity of the
matrices involved in the calculation process of the Paterson-Stockmeyer (PS)
scheme. Based on the error analysis considering the transaction error and the
error introduced by filtering, the proposed algorithm can obtain similar
accuracy as the original PS scheme but is more efficient than it. For the
near-sparse matrix power series, the proposed method is also more efficient
than the MATLAB built-in codes.
