A Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems (Journal of Computational Mathematics, 2018)
The preconditioner for parameterized inexact Uzawa methods has been used to solvesome indefinite saddle point problems. Firstly, we modify the preconditioner by making itmore generalized, then we use theoretical analyses to show that the iteration method convergesunder certain conditions. Moreover, we discuss the optimal parameter and matricesbased on these conditions. Finally, we propose two improved methods. Numerical experimentsare provided to show the effectiveness of the modified preconditioner. All methodshave fantastic convergence rates by choosing the optimal parameter and matrices.
Keywords: Preconditioner; Inexact Uzawa method; Saddle point problems; Indefiniteness; Convergence.