Extended shift-splitting preconditioners for saddle point problems

Zheng, Qingqing; Lu, Linzhang

doi:10.1016/j.cam.2016.09.008

Cited by 15 publications

(12 citation statements)

References 36 publications

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“…(a) When A is HPD, the P SS preconditioner was studied in [15] and P GSS preconditioner is studied in [21,32,34]. Moreover the P ESS preconditioner was presented in [45].…”

Section: Semi-convergence Of Epss Iteration Methodsmentioning

confidence: 99%

An extension of the positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems

Masoudi

Salkuyeh

2020

Computers & Mathematics with Applications

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“…(a) When A is HPD, the P SS preconditioner was studied in [15] and P GSS preconditioner is studied in [21,32,34]. Moreover the P ESS preconditioner was presented in [45].…”

Section: Semi-convergence Of Epss Iteration Methodsmentioning

confidence: 99%

An extension of the positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems

Masoudi

Salkuyeh

2020

Computers & Mathematics with Applications

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“…Obviously if H = αI and Q = αI, then the MGSS method reduces to the shift-splitting method, and H = αI and Q = βI, then the MGSS method coincides with the GSS method. In [24], when the matrix A is symmetric positive definite the convergence of the iterative method (6) was investigated. Denoting Γ = M −1 N and h = M −1 b, the iterative method (5) can be rewritten as…”

Section: The Mgss Iterative Methodsmentioning

confidence: 99%

A modification of the generalized shift-splitting method for singular saddle point problems

Salkuyeh

Rahimian

2017

Computers & Mathematics with Applications

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Abstract. A modification of the generalized shift-splitting (GSS) method is presented for solving singular saddle point problems. In this kind of modification, the diagonal shift matrix is replaced by a block diagonal matrix which is symmetric positive definite. Semiconvergence of the proposed method is investigated. The induced preconditioner is applied to the saddle point problem and the preconditioned system is solved by the restarted generalized minimal residual method. Eigenvalue distribution of the preconditioned matrix is also discussed. Finally some numerical experiments are given to show the effectiveness and robustness of the new preconditioner. Numerical results show that the modified GSS method is superior to the classical GSS method.

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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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Extended shift-splitting preconditioners for saddle point problems

Cited by 15 publications

References 36 publications

An extension of the positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems

An extension of the positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems

A modification of the generalized shift-splitting method for singular saddle point problems

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

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