A generalization of preconditioned parameterized inexact Uzawa method for indefinite saddle point problems

The parameterized inexact Uzawa methods have been used to solve some of the symmetric saddle point problems. In this paper, a new preconditioned parameterized inexact Uzawa method is presented to solve indefinite saddle point problems. After preconditioning, theoretical analyses show that the iteration method converges under certain conditions. So we propose three new algorithms based on these conditions. Numerical experiments are provided to show the effectiveness of the proposed preconditioner and all these algorithms have fantastic convergence rates by choosing optimal parameters.