A modified symmetric successive overrelaxation method for augmented systems

Darvishi, M. T.; Hessari, Peyman

doi:10.1016/j.camwa.2011.03.103

Cited by 32 publications

(11 citation statements)

References 16 publications

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“…In 2008, Zhang and Lu [29] discussed the generalized symmetric SOR method. In 2011, Darvishi and Hessari [11] discussed the modified SSOR iterative method. In 2012, Martins et al [20] presented a modified accelerated overrelaxation iterative method.…”

Section: Introductionmentioning

confidence: 99%

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%

Accelerated SOR-like method for augmented linear systems

Njeru

Guo

2015

Bit Numer Math

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“…The authors of [15,34], considered the following splitting: where Q being nonsingular symmetric, α, β ∈ R, α + β = 1, and applied the symmetric SOR method to solve Equation (1).…”

Section: A New Modified Ssor Iteration Methodsmentioning

confidence: 99%

“…Table 2 represents the numerical performance of the MSSOR-like, as well as our method, when all eigenvalues of Note that, since the explicit expressions of parameters cannot be obtained, we only choose them by trial and error. Similar approach has been followed in other SSOR methods [14,15,34,40,43]. However, in order to analyse the performance of our method for the values of β = −1.5 and β = 1.5, we consider a range of values for the two parameters w and α in the intervals of (0, 2) and (0, 2), respectively, in 0.1 steps.…”

Section: Numerical Experimentsmentioning

confidence: 95%

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A new modified SSOR iteration method for solving augmented linear systems

Najafi

Edalatpanah

2013

International Journal of Computer Mathematics

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In this paper, we present a new symmetric successive over-relaxation method to find solution of the large sparse augmented linear systems, which is the extension of the symmetric successive overrelaxation iteration method. The convergence analysis of our method is also studied. Furthermore, the functional equation between the parameters and the eigenvalues of the relevant iteration matrix is obtained. Finally, numerical computations are presented to show the effectiveness of our algorithm.

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“…We assume that the system has a unique solution and the equations are ordered so that, a ii ≠0, (Darvishi and Hessari, 2011;Papadomanolaki et al, 2010;Wang, 2010;Louka et al, 2009;Salkuyeh and Toutounian, 2006). Jacobi method is the simplest known iterative method; it is a direct application of the fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

On the Successive Overrelaxation Method

Youssef¹

2012

Journal of Mathematics and Statistics

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Problem statement:A new variant of the Successive Overrelaxation (SOR) method for solving linear algebraic systems, the KSOR method was introduced. The treatment depends on the assumption that the current component can be used simultaneously in the evaluation in addition to the use the most recent calculated components as in the SOR method. Approach: Using the hidden explicit characterization of linear functions to introduce a new version of the SOR, the KSOR method. Prove the convergence and the consistency analysis of the proposed method. Test the method through application to well-known examples. Results: The proposed method had the advantage of updating the first component in the first equation from the first step which affected all the subsequent calculations. It was proved that the KSOR can converge for all possible values of the relaxation parameter, ω*∈R-[-2, 0] not only for (ω∈(0, 2) as in the SOR method. A new eigenvalue functional relation similar to that of the SOR method between the eigenvalues of the iteration matrices of the Jacobi and the KSOR methods was proved. Numerical examples illustrating this treatment, comparison with the SOR with optimal values of the relaxation parameter were considered. Conclusion: The relaxation parameter ω* in the proposed method, can take values, ω*∈R-[-2, 0] not only for (ω∈(0, 2) as in the SOR. The enlargement of the domain has the affect of relaxing the sensivity near the optimum value of the relaxation parameter. Moreover, all the advantages of the SOR method are conserved and the proposed method can be applied to any system. This approach is promising and will help in the numerical treatment of boundary value problems. Other extensions and applications for further work are mentioned.

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A modified symmetric successive overrelaxation method for augmented systems

Cited by 32 publications

References 16 publications

Accelerated SOR-like method for augmented linear systems

Accelerated SOR-like method for augmented linear systems

A new modified SSOR iteration method for solving augmented linear systems

On the Successive Overrelaxation Method

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