Symmetric accelerated overrelaxation (SAOR) method

In this article, we develop symmetric block successive overrelaxation (S-block-SOR) methods for finding the solution of the rank-deficient least squares problems. We propose an S2-block-SOR and an S3-block-SOR method for solving such problems and the convergence of these two methods is studied. The comparisons between the S2-block and the S3-block methods are presented with some numerical examples.

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“…Let x (k) be kth approximation of solution (3) by SOR method using splitting (4). In symmetric SOR we obtain x (k+1/2) as follows [5]:…”

Section: Preparatory Knowledgementioning

confidence: 99%

Symmetric block-SOR methods for rank-deficient least squares problems

Darvishi¹,

Khani²,

Hamedi-Nezhad³

et al. 2008

Journal of Computational and Applied Mathematics

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“…Better dynamical realizations of the symmetric successive over-relaxation (SSOR), the accelerated over-relaxation (AOR), and the symmetric accelerated over-relaxation (SAOR) methods [1][2][3][4] are offered in the paper to solve the following:…”

Section: Introductionmentioning

confidence: 99%

“…Tian [13] developed the AOR method for non-square linear systems. Many works were developed for the better convergence behavior analyses of the SSOR, AOR, and SAOR methods [2,3,14]. Liu [15] applied the minimization technique in Equation (6) to search for the optimal value of the relaxation parameter used in the SOR at each iteration step.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Optimal Values of Parameters in the SSOR, AOR, and SAOR Testing Using Poisson Linear Equations

Liu,

El-Zahar,

Chang

2023

Mathematics

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This paper proposes a dynamical approach to determine the optimal values of the parameters used in each iteration of the symmetric successive over-relaxation (SSOR), accelerated over-relaxation (AOR), and symmetric accelerated over-relaxation (SAOR) methods for solving linear equation systems. When the optimal values of the parameters in the SSOR, AOR, and SAOR are hard to determine as some fixed values, they are obtained by minimizing the merit functions, which are based on the maximal projection technique between the left- and right-hand-side vectors, which involves the input vector, the previous step values of the variables, and the parameters. The novelty is a new concept of the dynamical optimal values of the parameters, instead of the fixed values and the maximal projection technique. In a preferred range, the optimal values of the parameters can be quickly determined by using the golden section search algorithm with a loose convergence criterion. Without knowing and having the theoretical optimal values in general, the new methods might provide an alternative and proper choice of the values of the parameters for accelerating the convergence speed. Numerical testings of the linear Poisson equation discretized to a matrix–vector form and a Lyapunov equation form were used to assess the performance of the DOSSOR, DOAOR, and DOSAOR dynamical optimal methods.

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“…Also, Zhang and Lu [12] presented the generalized symmetric SOR (GSSOR) method for solving large sparse augmented systems. One may find details of symmetric iterative methods to solve different kinds of linear systems in [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

A modified symmetric successive overrelaxation method for augmented systems

Darvishi

Hessari

2011

Computers & Mathematics with Applications

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a b s t r a c tIn this paper, we establish a modified symmetric successive overrelaxation (MSSOR) method, to solve augmented systems of linear equations, which uses two relaxation parameters. This method is an extension of the symmetric SOR (SSOR) iterative method. The convergence of the MSSOR method for augmented systems is studied. Numerical examples show that the new method is an efficient method.

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Symmetric accelerated overrelaxation (SAOR) method

Cited by 28 publications

References 4 publications

Symmetric block-SOR methods for rank-deficient least squares problems

Symmetric block-SOR methods for rank-deficient least squares problems

Dynamical Optimal Values of Parameters in the SSOR, AOR, and SAOR Testing Using Poisson Linear Equations

A modified symmetric successive overrelaxation method for augmented systems

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