Optimization of the parameterized Uzawa preconditioners for saddle point matrices
نویسنده
چکیده
The parameterized Uzawa preconditioners for saddle point problems are studied in this paper. The eigenvalues of the preconditioned matrix are located in (0, 2) by choosing the suitable parameters. Furthermore, we give two strategies to optimize the rate of convergence by finding the suitable values of parameters. Numerical computations show that the parameterized Uzawa preconditioners can lead to practical and effective preconditioned GMRES methods for solving the saddle point problems. © 2008 Elsevier B.V. All rights reserved.
منابع مشابه
Performance Analysis of a Special GPIU Method for Singular Saddle Point Problems
In this paper, we first provide semi-convergence analysis for a special GPIU(Generalized Parameterized Inexact Uzawa) method with singular preconditioners for solving singular saddle point problems. We next provide a methodology of how to choose nearly quasi-optimal parameters of the special GPIU method. Lastly, numerical experiments are carried out to examine the effectiveness of the special G...
متن کاملAcceleration of One-parameter Relaxation Methods for Singular Saddle Point Problems
In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR m...
متن کاملPerformance Comparison of Relaxation Methods with Singular and Nonsingular Preconditioners for Singular Saddle Point Problems
In this paper, we first review the PU and Uzawa-SAOR relaxation methods with singular or nonsingular preconditioning matrices for solving singular saddle point problems, and then we provide numerical experiments to compare performance results of the relaxation iterative methods using nonsingular preconditioners with those using singular preconditioners. Mathematics Subject Classification: 65F10...
متن کاملA New Analysis of Block Preconditioners for Saddle Point Problems
We consider symmetric saddle point matrices. We analyze block preconditioners based on the knowledge of a good approximation for both the top left block and the Schur complement resulting from its elimination. We obtain bounds on the eigenvalues of the preconditioned matrix that depend only of the quality of these approximations, as measured by the related condition numbers. Our analysis applie...
متن کاملA Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems
The preconditioner for parameterized inexact Uzawa methods have been used to solve some indefinite saddle point problems. Firstly, we modify the preconditioner by making it more generalized, then we use theoretical analyses to show that the iteration method converges under certain conditions. Moreover, we discuss the optimal parameter and matrices based on these conditions. Finally, we propose ...
متن کامل