In this paper, we present a new convergence upper bound for the greedy Gauss-Seidel (GGS) method proposed by Zhang and Li [38]. The new convergence upper bound improves the upper bound of the GGS method. In addition, we also propose a novel greedy block Gauss-Seidel (RDBGS) method based on the greedy strategy of the GGS method for solving large linear least-squares problems. It is proved that the RDBGS method converges to the unique solution of the linear least-squares problem. Numerical experiments demonstrate that the RDBGS method has superior performance in terms of iteration steps and computation time.
