Optimization of a parameterized inexact Uzawa method for saddle point problems

Xu, Yufeng; Yang, Li

doi:10.1080/00207160.2017.1411592

Cited by 2 publications

(1 citation statement)

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“…ere are many ways to solve the saddle point linear problem [3,[17][18][19][20][21][22][23][24][25]. Recently, Cao et al [26][27][28][29] proposed a method which is based on the shift-splitting iteration method presented by Bai et al [30] to solve the saddle-point problem.…”

Section: Introductionmentioning

confidence: 99%

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

Xiao

Zhang

2021

Journal of Mathematics

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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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