Generalized successive overrelaxation iterative method for a class of complex symmetric linear system of equations

Salkuyeh, Davod Khojasteh; Hezari, Davod; Edalatpour, Vahid

doi:10.1080/00207160.2014.912753

Cited by 92 publications

(55 citation statements)

References 24 publications

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“…Remark 2 From Theorem 2, we see that the optimal convergence factor of the SSOR method here is the same as that of the GSOR method in [27]. However, the SSOR method has two choices for the optimal iteration parameter but the GSOR method has only a single choice.…”

Section: Fig 1 Condition For Minimization Of ρ(H ω )mentioning

confidence: 84%

“…Besides, we know that the GSOR method is convergent if 0 < ω < 2 1+ρ(S) from Theorem 1 in [27]. So the convergence interval length of the GSOR method is 2 1+ρ(S) .…”

Section: Theoremmentioning

confidence: 93%

“…Lemma 2 [27] Let the matrices W and T ∈ R n×n be symmetric positive definite and symmetric, respectively. Then the eigenvalues of the matrix S := W −1 T are all real.…”

Section: The Optimal Parameters Of the Ssor Methodsmentioning

confidence: 99%

“…A large variety of effective iteration methods have been proposed in the literature for solving the linear system (1), such as C-to-R iteration methods [1,2,5,12,17], preconditioned Krylov subspace methods [14,16,26], splitting iteration methods [11,14,22,23,27,31], Hermitian and skew-Hermitian splitting (HSS) method and its variants [4, 6-9, 18, 21, 24, 30].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On SSOR iteration method for a class of block two-by-two linear systems

Liang

Zhang

2015

Numer Algor

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In this paper, the optimal iteration parameters of the symmetric successive overrelaxation (SSOR) method for a class of block two-by-two linear systems are obtained, which result in optimal convergence factor. An accelerated variant of the SSOR (ASSOR) method is presented, which significantly improves the convergence rate of the SSOR method. Furthermore, a more practical way to choose iteration parameters for the ASSOR method has also been proposed. Numerical experiments demonstrate the efficiency of the SSOR and ASSOR methods for solving a class of block two-by-two linear systems with the optimal parameters.

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Section: Fig 1 Condition For Minimization Of ρ(H ω )mentioning

confidence: 84%

“…Besides, we know that the GSOR method is convergent if 0 < ω < 2 1+ρ(S) from Theorem 1 in [27]. So the convergence interval length of the GSOR method is 2 1+ρ(S) .…”

Section: Theoremmentioning

confidence: 93%

“…Lemma 2 [27] Let the matrices W and T ∈ R n×n be symmetric positive definite and symmetric, respectively. Then the eigenvalues of the matrix S := W −1 T are all real.…”

Section: The Optimal Parameters Of the Ssor Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On SSOR iteration method for a class of block two-by-two linear systems

Liang

Zhang

2015

Numer Algor

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“…For more practical backgrounds of this class of problems, see [2,11,13]. Recently, Salkuyeh et al [23] applied the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system (2). The GSOR iteration method can be described as follows:…”

Section: Mjommentioning

confidence: 99%

Two Efficient Inexact Algorithms for a Class of Large Sparse Complex Linear Systems

2015

Self Cite

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Recently Salkuyeh et al. (Int J Comput Math 92:802-815, 2015) studied the generalized SOR (GSOR) iterative method for a class of complex symmetric linear system of equations. In this paper, we present an inexact variant of the GSOR method in which the conjugate gradient and the preconditioned conjugate gradient methods are regarded as its inner iteration processes at each step of the GSOR outer iteration. Moreover, we construct a new method called shifted GSOR iteration method which is obtained from combination of a shiftsplitting iteration scheme and the GSOR iteration method. The convergence analysis of the proposed methods are presented. Some numerical experiments are given to show the performance of the methods and are compared with those of the inexact MHSS method.Mathematics Subject Classification. 65F10, 93C10.

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Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations

Hezari

Edalatpour

Salkuyeh

2015

Numerical Linear Algebra App

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In this paper, we present a preconditioned variant of the generalized successive overrelaxation (GSOR) iterative method for solving a broad class of complex symmetric linear systems. We study conditions under which the spectral radius of the iteration matrix of the preconditioned GSOR method is smaller than that of the GSOR method and determine the optimal values of iteration parameters. Numerical experiments are given to verify the validity of the presented theoretical results and the effectiveness of the preconditioned GSOR method.

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Generalized successive overrelaxation iterative method for a class of complex symmetric linear system of equations

Cited by 92 publications

References 24 publications

On SSOR iteration method for a class of block two-by-two linear systems

On SSOR iteration method for a class of block two-by-two linear systems

Two Efficient Inexact Algorithms for a Class of Large Sparse Complex Linear Systems

Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations

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