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

摘要

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.