Optimal parameters of the generalized symmetric SOR method for augmented systems

Chao, Zhen; Zhang, Naimin; Lu, Yunzeng

doi:10.1016/j.cam.2014.01.023

Cited by 26 publications

(26 citation statements)

References 21 publications

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“…In 2012, Martins et al [20] presented a modified accelerated overrelaxation iterative method. In 2014, Chao et al [10] studied the optimal parameters of the GSSOR method and presented the convergence analysis of the method.…”

Section: Introductionmentioning

confidence: 99%

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Accelerated SOR-like method for augmented linear systems

Njeru

Guo

2015

Bit Numer Math

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By accelerating the SOR-like method by two parameters alpha and omega, we propose an accelerated SOR-like (ASOR) method for solving the augmented linear systems. The convergence of the ASOR method is discussed under suitable restrictions on the iteration parameters alpha and omega, and the experimental optimal values of the iteration parameters are determined. Numerical results are presented to show the efficiency of the ASOR method when the iteration parameters alpha and omega are suitably chosen.

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Section: Introductionmentioning

confidence: 99%

“…3. A comparison between the results obtained with ASOR method and those obtained with SOR-like method [16], GSOR method [7] and GSSOR method [10] are given to show the efficiency of the ASOR method over SOR-like, GSOR and GSSOR methods.…”

Section: Introductionmentioning

confidence: 99%

Accelerated SOR-like method for augmented linear systems

Njeru

Guo

2015

Bit Numer Math

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“…Let µ be an eigenvalue of Q −1 B T A −1 B and λ be an eigenvalue of T ω,1 . From equation (6), one can obtain the following quadratic equation for λ…”

Section: Theorem 22 ([4]mentioning

confidence: 99%

“…Many relaxation iterative methods for solving the nonsingular saddle point problem have been proposed. For example, Golub et al [10] proposed the SOR-like method and presented an incomplete formula for finding one optimal parameter, Bai et al [3] proposed the GSOR (Generalized SOR) method and presented a formula for finding two optimal parameters for the GSOR and a complete formula for finding one optimal parameter for SOR-like method, Wu et al [15] proposed the MSSOR (Modified symmetric SOR) method, Zhang and Lu [20] studied the GSSOR (Generalized symmetric SOR) method and Chao et al [6] presented a formula for finding two optimal parameters for the GSSOR, Yun studied several variants of Uzawa method [18,19], and so on.…”

Section: Introductionmentioning

confidence: 99%

Acceleration of One-Parameter Relaxation Methods for Singular Saddle Point Problems

Yun¹

2016

Journal of the Korean Mathematical Society

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Abstract. In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR methods with scaled preconditioners by comparing their performance with the parameterized Uzawa method with optimal parameters.

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“…For this case, many relaxation iterative methods based on matrix splittings and their convergence properties have been proposed and analyzed, e.g., SOR-like method [11], GSOR (Generalized SOR) method [2], PIU (Parameterized Inexact Uzawa) method [3], SSOR-like method [8,20], GSSOR (Generalized SSOR) method [7,18], several variants of Uzawa method [16,17], and so on.…”

Section: Introductionmentioning

confidence: 99%