  In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularized least
squares regression ($l_q$LS) has received considerable attention due to its
superiorities on sparsity-inducing and bias-reduction over the convex
counterparts. In this paper, we propose a Gauss-Seidel iterative thresholding
algorithm (called GAITA) for solution to this problem. Different from the
classical iterative thresholding algorithms using the Jacobi updating rule,
GAITA takes advantage of the Gauss-Seidel rule to update the coordinate
coefficients. Under a mild condition, we can justify that the support set and
sign of an arbitrary sequence generated by GAITA will converge within finite
iterations. This convergence property together with the Kurdyka-{\L}ojasiewicz
property of ($l_q$LS) naturally yields the strong convergence of GAITA under
the same condition as above, which is generally weaker than the condition for
the convergence of the classical iterative thresholding algorithms.
Furthermore, we demonstrate that GAITA converges to a local minimizer under
certain additional conditions. A set of numerical experiments are provided to
show the effectiveness, particularly, much faster convergence of GAITA as
compared with the classical iterative thresholding algorithms.
