scholarly journals A modified generalized shift-splitting preconditioner for nonsymmetric saddle point problems

2017 ◽  
Vol 78 (1) ◽  
pp. 297-331 ◽  
Author(s):  
Zheng-Ge Huang ◽  
Li-Gong Wang ◽  
Zhong Xu ◽  
Jing-Jing Cui
Keyword(s):  
Saddle Point ◽  
Saddle Point Problems ◽  
Generalized Shift

scholarly journals Parameterized generalized shift-splitting preconditioners for nonsymmetric saddle point problems

2018 ◽  
Vol 75 (2) ◽  
pp. 349-373 ◽  
Author(s):  
Zheng-Ge Huang ◽  
Li-Gong Wang ◽  
Zhong Xu ◽  
Jing-Jing Cui
Keyword(s):  
Saddle Point ◽  
Saddle Point Problems ◽  
Generalized Shift

scholarly journals Newton-PGSS and Its Improvement Method for Solving Nonlinear Systems with Saddle Point Jacobian Matrices

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Yao Xiao ◽  
Qingbiao Wu ◽  
Yuanyuan Zhang
Keyword(s):  
Nonlinear System ◽  
Saddle Point ◽  
Convergence Analysis ◽  
Local Convergence ◽  
Semilocal Convergence ◽  
Saddle Point Problems ◽  
Jacobian Matrices ◽  
Improvement Method ◽  
Generalized Shift ◽  
Local Convergence Analysis

The preconditioned generalized shift-splitting (PGSS) iteration method is unconditionally convergent for solving saddle point problems with nonsymmetric coefficient matrices. By making use of the PGSS iteration as the inner solver for the Newton method, we establish a class of Newton-PGSS method for solving large sparse nonlinear system with nonsymmetric Jacobian matrices about saddle point problems. For the new presented method, we give the local convergence analysis and semilocal convergence analysis under Hölder condition, which is weaker than Lipschitz condition. In order to further raise the efficiency of the algorithm, we improve the method to obtain the modified Newton-PGSS and prove its local convergence. Furthermore, we compare our new methods with the Newton-RHSS method, which is a considerable method for solving large sparse nonlinear system with saddle point nonsymmetric Jacobian matrix, and the numerical results show the efficiency of our new method.

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