  Precision matrix estimation is an important problem in statistical data
analysis. This paper introduces a fast sparse precision matrix estimation
algorithm, namely GISS$^{{\rho}}$, which is originally introduced for
compressive sensing. The algorithm GISS$^{{\rho}}$ is derived based on $l_1$
minimization while with the computation advantage of greedy algorithms. We
analyze the asymptotic convergence rate of the proposed GISS$^{{\rho}}$ for
sparse precision matrix estimation and sparsity recovery properties with
respect to the stopping criteria. Finally, we numerically compare GISS$^{\rho}$
to other sparse recovery algorithms, such as ADMM and HTP in three settings of
precision matrix estimation. The numerical results show the advantages of the
proposed algorithm.
