  In this paper, two new efficient algorithms for calculating the sign function
of the large-scale sparse matrix are proposed by combining filtering algorithm
with Newton method and Newton Schultz method respectively. Through the
theoretical analysis of the error diffusion in the iterative process, we
designed an adaptive filtering threshold, which can ensure that the filtering
has little impact on the iterative process and the calculation result.
Numerical experiments are consistent with our theoretical analysis, which shows
that the computational efficiency of our method is much better than that of
Newton method and Newton Schultz method, and the computational error is of the
same order of magnitude as that of the two methods.
