  Identifying influential nodes in networks is a significant and challenging
task. Among many centrality indices, the $k$-shell index performs very well in
finding out influential spreaders. However, the traditional method for
calculating the $k$-shell indices of nodes needs the global topological
information, which limits its applications in large-scale dynamically growing
networks. Recently, L\@\"{u} \emph{et al.} [Nature Communications 7 (2016)
10168] proposed a novel asynchronous algorithm to calculate the $k$-shell
indices, which is suitable to deal with large-scale growing networks. In this
paper, we propose two algorithms to select nodes and update their intermediate
values towards the $k$-shell indices, which can help in accelerating the
convergence of the calculation of $k$-shell indices. The former algorithm takes
into account the degrees of nodes while the latter algorithm prefers to choose
the node whose neighbors' values have been changed recently. We test these two
methods on four real networks and three artificial networks. The results
suggest that the two algorithms can respectively reduce the convergence time up
to 75.4\% and 92.9\% in average, compared with the original asynchronous
updating algorithm.
