Accelerated Overrelaxation Method

Hadjidimos, A.

doi:10.2307/2006264

Cited by 28 publications

(33 citation statements)

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“…In 1978, AOR iterative method was introduced by Hadjidimos [14] as two-parameter generalization of the SOR method. According to equation (18), the general form of AOR iterative method can be defined as…”

Section: Aor Iterative Methodsmentioning

confidence: 99%

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Cubic B-spline solution for two-point boundary value problem with AOR iterative method

Suardi

Radzuan

Sulaiman

2017

J. Phys.: Conf. Ser.

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Abstract. In this study, the cubic B-spline approximation equation has been derived by using the cubic B-spline discretization scheme to solve two-point boundary value problems. In addition to that, system of cubic B-spline approximation equations is generated from this spline approximation equation in order to get the numerical solutions. To do this, the Accelerated Over Relaxation (AOR) iterative method has been used to solve the generated linear system. For the purpose of comparison, the GS iterative method is designated as a control method to compare between SOR and AOR iterative methods. There are two examples of proposed problems that have been considered to examine the efficiency of these proposed iterative methods via three parameters such as their number of iterations, computational time and maximum absolute error. The numerical results are obtained from these iterative methods, it can be concluded that the AOR iterative method is slightly efficient as compared with SOR iterative method. IntroductionBoundary value problems plays a important roles to apply and solve many application of science and engineering phenomenan. Researchers in science, physics and engineering get more advantages from the numerical solutions which obtained from the two-point boundary value problems. Actually there are various methods are used to get the solutions in boundary value problems such as families of Galerkin methods namely Sinc-Galerkin method [1] and hybrid Galerkin method [2], Adomain decomposition method [3] and shooting method [4]. The other researchers also have been used the families of B-spline [5,6,7] to solve the same problems. B-spline scheme was considered in this paper to apply with the aim of discretizing the proposed problem.To obtain the cubic B-spline approximation equation of the proposed problem, firstly, the proposed problem needs to be discretized via family of spline or more specifically by imposing cubic B-spline discretization scheme. Then the approximation equation can be derived and used to contruct a linear system. Next, in this paper, the linear system can be solved via the iterative methods. This is because of motivation given by Young [8], Hackbush [9] and Saad [10] in which they have been proposed and discussed about the various iterative methods to solve any linear system.As mentioned in the second paragraph, the utmost objective of this paper is used the cubic Bspline approximation equation to solve two-point boundary value problem with attention to investigate the application of AOR iterative method. To analyze the performance of AOR, the implementation of the SOR iteration family method has been used as control methods.

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Section: Aor Iterative Methodsmentioning

confidence: 99%

“…The AOR iterative method can be reduced into another iterative methods if the parameters ω1 and ω2 are set up in specific value [14,15]. For example, when ω2, ω1 takes 1, 0 , 1, 1 , ω2, 0 or (ω1, ω1), the AOR will reduces into Jacobi, Gauss Seidel, Simultaneous Overrelaxation and Successive Overrelaxation respectively.…”

Section: Aor Iterative Methodsmentioning

confidence: 99%

Cubic B-spline solution for two-point boundary value problem with AOR iterative method

Suardi

Radzuan

Sulaiman

2017

J. Phys.: Conf. Ser.

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“…1 , / is taken to be . , /, .1, 1/ and .0, 1/, we obtain the generalized SOR, the generalized Guass-Seidel and the generalized Jacobi iteration methods, respectively; see [7,17]. When !…”

Section: Methods 11 (The Gsts Iteration Method)mentioning

confidence: 99%

“…First of all, we present the GSTS iteration method for the saddle-point linear system (17). The Hermitian and the skew-Hermitian parts of the matrix A are given by…”

Section: Extension To Saddle-point Linear Systemsmentioning

confidence: 99%

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Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems

Krukier

Ren

2013

Numer. Linear Algebra Appl.

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A generalized skew-Hermitian triangular splitting iteration method is presented for solving non-Hermitian linear systems with strong skew-Hermitian parts. We study the convergence of the generalized skew-Hermitian triangular splitting iteration methods for non-Hermitian positive definite linear systems, as well as spectrum distribution of the preconditioned matrix with respect to the preconditioner induced from the generalized skew-Hermitian triangular splitting. Then the generalized skew-Hermitian triangular splitting iteration method is applied to non-Hermitian positive semidefinite saddle-point linear systems, and we prove its convergence under suitable restrictions on the iteration parameters. By specially choosing the values of the iteration parameters, we obtain a few of the existing iteration methods in the literature. Numerical results show that the generalized skew-Hermitian triangular splitting iteration methods are effective for solving non-Hermitian saddle-point linear systems with strong skew-Hermitian parts.

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Modulus‐based synchronous multisplitting iteration methods for linear complementarity problems

Bai

Zhang

2012

Numerical Linear Algebra App

138

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By an equivalent reformulation of the linear complementarity problem into a system of fixed-point equations, we construct modulus-based synchronous multisplitting iteration methods based on multiple splittings of the system matrix. These iteration methods are suitable to high-speed parallel multiprocessor systems and include the multisplitting relaxation methods such as Jacobi, Gauss-Seidel, successive overrelaxation, and accelerated overrelaxation of the modulus type as special cases. We establish the convergence theory of these modulus-based synchronous multisplitting iteration methods and their relaxed variants when the system matrix is an H C -matrix. Numerical results show that these new iteration methods can achieve high parallel computational efficiency in actual implementations.

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Accelerated Overrelaxation Method

Cited by 28 publications

References 0 publications

Cubic B-spline solution for two-point boundary value problem with AOR iterative method

Cubic B-spline solution for two-point boundary value problem with AOR iterative method

Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems

Modulus‐based synchronous multisplitting iteration methods for linear complementarity problems

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