A New GSOR Method for Generalised Saddle Point Problems

2016 ◽  
Vol 6 (1) ◽  
pp. 23-41 ◽  
Author(s):  
Na Huang ◽  
Chang-Feng Ma
Keyword(s):  
Saddle Point ◽  
Coefficient Matrix ◽  
Numerical Results ◽  
Saddle Point Problems ◽  
Successive Overrelaxation ◽  
Iteration Parameters

AbstractA novel generalised successive overrelaxation (GSOR) method for solving generalised saddle point problems is proposed, based on splitting the coefficient matrix. The proposed method is shown to converge under suitable restrictions on the iteration parameters, and we present some illustrative numerical results.

scholarly journals Generalized ASOR and Modified ASOR Methods for Saddle Point Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-18
Author(s):  
Zhengge Huang ◽  
Ligong Wang ◽  
Zhong Xu ◽  
Jingjing Cui
Keyword(s):  
Saddle Point ◽  
Convergence Rates ◽  
Sufficient Conditions ◽  
Optimal Parameters ◽  
Saddle Point Problems ◽  
Successive Overrelaxation ◽  
Numerical Examples ◽  
Singular Saddle Point Problems ◽  
Iteration Parameters

Recently, the accelerated successive overrelaxation- (SOR-) like (ASOR) method was proposed for saddle point problems. In this paper, we establish a generalized accelerated SOR-like (GASOR) method and a modified accelerated SOR-like (MASOR) method, which are extension of the ASOR method, for solving both nonsingular and singular saddle point problems. The sufficient conditions of the convergence (semiconvergence) for solving nonsingular (singular) saddle point problems are derived. Finally, numerical examples are carried out, which show that the GASOR and MASOR methods have faster convergence rates than the SOR-like, generalized SOR (GSOR), modified SOR-like (MSOR-like), modified symmetric SOR (MSSOR), generalized symmetric SOR (GSSOR), generalized modified symmetric SOR (GMSSOR), and ASOR methods with optimal or experimentally found optimal parameters when the iteration parameters are suitably chosen.

scholarly journals A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wei-Hua Luo ◽  
Ting-Zhu Huang
Keyword(s):  
Saddle Point ◽  
Unit Circle ◽  
Iterative Methods ◽  
Krylov Subspace ◽  
Numerical Results ◽  
Saddle Point Problems ◽  
Good Convergence ◽  
Stokes Problems ◽  
Preconditioned Matrix ◽  
Generalized Saddle Point Problems

By using Sherman-Morrison-Woodbury formula, we introduce a preconditioner based on parameterized splitting idea for generalized saddle point problems which may be singular and nonsymmetric. By analyzing the eigenvalues of the preconditioned matrix, we find that whenαis big enough, it has an eigenvalue at 1 with multiplicity at leastn, and the remaining eigenvalues are all located in a unit circle centered at 1. Particularly, when the preconditioner is used in general saddle point problems, it guarantees eigenvalue at 1 with the same multiplicity, and the remaining eigenvalues will tend to 1 as the parameterα→0. Consequently, this can lead to a good convergence when some GMRES iterative methods are used in Krylov subspace. Numerical results of Stokes problems and Oseen problems are presented to illustrate the behavior of the preconditioner.

A New Uzawa-Type Iteration Method for Non-Hermitian Saddle-Point Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 211-226
Author(s):  
Yan Dou ◽  
Ai-Li Yang ◽  
Yu-Jiang Wu
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Spectral Properties ◽  
Numerical Results ◽  
Saddle Point Problems ◽  
Convergence Properties ◽  
Saddle Point Matrix

AbstractBased on a preconditioned shift-splitting of the (1,1)-block of non-Hermitian saddle-point matrix and the Uzawa iteration method, we establish a new Uzawa-type iteration method. The convergence properties of this iteration method are analyzed. In addition, based on this iteration method, a preconditioner is proposed. The spectral properties of the preconditioned saddle-point matrix are also analyzed. Numerical results are presented to verify the robustness and the efficiency of the new iteration method and the preconditioner.

Generalized Accelerated Hermitian and Skew-Hermitian Splitting Methods for Saddle-Point Problems

2017 ◽  
Vol 10 (1) ◽  
pp. 167-185 ◽  
Author(s):  
H. Noormohammadi Pour ◽  
H. Sadeghi Goughery
Keyword(s):  
Saddle Point ◽  
Unique Solution ◽  
Numerical Experiments ◽  
Saddle Point Problem ◽  
Splitting Methods ◽  
Point Problem ◽  
Saddle Point Problems ◽  
Iteration Methods ◽  
Hss Iteration ◽  
Iteration Parameters

AbstractWe generalize the accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems. These methods involve four iteration parameters whose special choices can recover the preconditioned HSS and accelerated HSS iteration methods. Also a new efficient case is introduced and we theoretically prove that this new method converges to the unique solution of the saddle-point problem. Numerical experiments are used to further examine the effectiveness and robustness of iterations.

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