On parameterized block triangular preconditioners for generalized saddle point problems

Jiang, Mei-Qun; Cao, Yang; Yao, Lin‐Quan

doi:10.1016/j.amc.2009.12.026

Cited by 25 publications

(12 citation statements)

References 24 publications

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“…The eigenvalue estimates for AP −1 were provided, which improve some theoretical results appeared in the previous works such as [7,10]. When j < 0, the bounds for the real part of all the eigenvalues of AP −1 were mainly discussed.…”

Section: Introductionmentioning

confidence: 94%

“…A special case ofP when j < 0 was studied in [23][24][25]. The ideas of [10] and [22] were combined in [13], resulting in the generalized block triangular preconditioner…”

Section: Introductionmentioning

confidence: 99%

“…Krylov subspace methods together with various preconditioners are recommended for the saddle point problems in large scale. In the passed decades, there are lots of work on this topic, including block diagonal preconditioner [9,15,16,18], block triangular preconditioner [7,10,13,19,22,24], HSS preconditioner [1,2,4], constraint preconditioner [3,6,11], matrix splitting preconditioner [21] and so on.…”

Section: Introductionmentioning

confidence: 99%

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Eigenvalue analysis of a generalized indefinite block triangular preconditioner for generalized saddle point problems

Jin

2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 94%

“…A special case ofP when j < 0 was studied in [23][24][25]. The ideas of [10] and [22] were combined in [13], resulting in the generalized block triangular preconditioner…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Eigenvalue analysis of a generalized indefinite block triangular preconditioner for generalized saddle point problems

Jin

2015

Applied Mathematics and Computation

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“…So, a good preconditioner must be given as close as possible to the coefficient matrix. The preconditioners for saddle problems mainly can be considered in these cases, such as, block triangular preconditioners [2,22], block diagonal preconditioners [23][24][25], fully factorized two-by-two block matrix precoditioners [26,27], etc., see [28][29][30][31][32][33][34][35][36][37][38][39][40] for more detailed investigations.…”

Section: Introductionmentioning

confidence: 99%

A modified positive-definite and skew-Hermitian splitting preconditioner for generalized saddle point problems from the Navier-Stokes equation

Xie

2015

Numer Algor

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In this paper, we extend the relaxed positive-definite and skewHermitian splitting preconditioner (RPSS) for generalized saddle-point problems in [J.-L. Zhang, C.-Q. Gu and K. Zhang, Appl. Math. Comput. 249(2014)468-479] by introducing an additional parameter. The spectral properties of the presented new preconditioned matrix for generalized saddle-point problem are investigated, meanwhile, the infinite termination merit of the iterative step is also discussed if the Krylov subspace method preconditioned by the modified positive-definite and skewHermitian splitting preconditioner (MPSS) is applied. Some numerical experiments illustrate that the efficiency of the proposed new preconditioner.

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“…In the past few years, much work also has been devoted to developing efficient preconditioners for saddle point problems. A variety of preconditioners have been proposed and studied in many papers, such as block diagonal and block triangular preconditioners [7,19,20,24], constraint preconditioners [8,25], HSS-based preconditioners [3,6,12,13,30], dimensional split preconditioners [15,16], H−matrix preconditioners [17] and so on. In [14], Benzi, Golub and Liesen discussed a selection of numerical methods and useful preconditioners for saddle point problems.…”

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confidence: 99%

A Relaxed HSS Preconditioner for Saddle Point Problems from Meshfree Discretization

Cao¹,

Yao

Jiang

et al. 2013

JCM

Self Cite

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In this paper, a relaxed Hermitian and skew-Hermitian splitting (RHSS) preconditioner is proposed for saddle point problems from the element-free Galerkin (EFG) discretization method. The EFG method is one of the most widely used meshfree methods for solving partial differential equations. The RHSS preconditioner is constructed much closer to the coefficient matrix than the well-known HSS preconditioner, resulting in a RHSS fixed-point iteration. Convergence of the RHSS iteration is analyzed and an optimal parameter, which minimizes the spectral radius of the iteration matrix is described. Using the RHSS preconditioner to accelerate the convergence of some Krylov subspace methods (like GMRES) is also studied. Theoretical analyses show that the eigenvalues of the RHSS preconditioned matrix are real and located in a positive interval. Eigenvector distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are obtained. A practical parameter is suggested in implementing the RHSS preconditioner. Finally, some numerical experiments are illustrated to show the effectiveness of the new preconditioner.Mathematics subject classification: 65F10.

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On parameterized block triangular preconditioners for generalized saddle point problems

Cited by 25 publications

References 24 publications

Eigenvalue analysis of a generalized indefinite block triangular preconditioner for generalized saddle point problems

Eigenvalue analysis of a generalized indefinite block triangular preconditioner for generalized saddle point problems

A modified positive-definite and skew-Hermitian splitting preconditioner for generalized saddle point problems from the Navier-Stokes equation

A Relaxed HSS Preconditioner for Saddle Point Problems from Meshfree Discretization

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