Convergence analysis of the corrected Uzawa algorithm for symmetric saddle point problems

For the large sparse saddle point problems, Pan and Li recently proposed in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31(3): 231-242] a corrected Uzawa algorithm based on a nonlinear Uzawa algorithm with two nonlinear approximate inverses, and gave the detailed convergence analysis. In this paper, we focus on the convergence analysis of this corrected Uzawa algorithm, some inaccuracies in [H. K. Pan, W. Li, Math. Numer. Sinica, 2009, 31(3): 231-242] are pointed out, and a corrected convergence theorem is presented. A special case of this modified Uzawa algorithm is also discussed.