A necessary condition for the convergence of the accelerated overrelaxation (AOR) method

Yeyios, A.

doi:10.1016/0377-0427(89)90309-9

Cited by 10 publications

(9 citation statements)

References 10 publications

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“…The following theorem indicates a necessary condition for the convergence of this method ,in generally . This theorem has been proved in [19] for a crisp linear system. Here we prove this theorem for FLS and constructed matrix S.…”

Section: The Block Aor Iterative Methods For Fuzzy Linear Systemsmentioning

confidence: 94%

The Block Aor Iterative Methods For Solving Fuzzy Linear Systems

Najafi

Edalatpanah²

2012

J. Math. Computer Sci.

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Section: The Block Aor Iterative Methods For Fuzzy Linear Systemsmentioning

confidence: 94%

The Block Aor Iterative Methods For Solving Fuzzy Linear Systems

Najafi

Edalatpanah²

2012

J. Math. Computer Sci.

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“…The necessary condition for convergence of AOR method is formulated in work [32]. Let us rewrite method (18) in the form…”

Section: Convergence Of the Aor Methodsmentioning

confidence: 99%

Parallel Direct and Iterative Methods for Solving the Time-Fractional Diffusion Equation on Multicore Processors

2022

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The work is devoted to developing the parallel algorithms for solving the initial boundary problem for the time-fractional diffusion equation. After applying the finite-difference scheme to approximate the basis equation, the problem is reduced to solving a system of linear algebraic equations for each subsequent time level. The developed parallel algorithms are based on the Thomas algorithm, parallel sweep algorithm, and accelerated over-relaxation method for solving this system. Stability of the approximation scheme is established. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to compare these methods and to study the performance of parallel implementations. The parallel sweep method shows the lowest computing time.

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“…Solving systems of linear equations by iterative methods (such as Gauss Jacobi, Gauss-Seidel, Successive over relaxation (SOR), Accelerated over relaxation (AOR) method) involves the correction of one searched-for unknown value in every step by reducing the difference of a single individual equation; moreover, other equations in this process are not used. In order to accelerate the convergence of the iterative process, the methods are complemented by wellness principles which optimize the rate of the variable change in the iterative process [14].…”

Section: Introductionmentioning

confidence: 99%

“…Many authors have considered sufficient conditions for the convergence of the AOR method. To improve the convergence rate of the AOR method, the preconditioned AOR (PAOR) method has been considered by many authors [3,4,9,13].…”

Section: Introductionmentioning

confidence: 99%

Second Refinement of Accelerated over Relaxation Method for the Solution of Linear System

Assefa¹,

Teklehaymanot²

2021

PAMJ

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This paper describes a method for the numerical solution of linear system of equations. The main interest of refinement of accelerated over relaxation (RAOR) method is to minimize the spectral radius of the iteration matrix in order to increase the rate of convergence of the method comparing to the accelerated over relaxation (AOR) method. That is minimizing the spectral radius means increasing the rate of convergence of the method. This motivates us to refine the refinement of accelerated over relaxation method called second refinement of accelerated over relaxation method (SRAOR). In this paper, we proposed a second refinement of accelerated over relaxation method, which decreases the spectral radius of the iteration matrix significantly comparing to that of the refinement of accelerated over relaxation (RAOR) method. The method is a two-parameter generalization of the refinement of accelerated over relaxation methods and the optimal value of each parameter is derived. The third, fourth and in general the k th refinement of accelerated methods are also derived. The spectral radius of the iteration matrix and convergence criteria of the second refinement of accelerated over relaxation (SRAOR) are discussed. Finally a numerical example is given in order to see the efficiency of the proposed method comparing with that of the existing methods.

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A necessary condition for the convergence of the accelerated overrelaxation (AOR) method

Cited by 10 publications

References 10 publications

The Block Aor Iterative Methods For Solving Fuzzy Linear Systems

The Block Aor Iterative Methods For Solving Fuzzy Linear Systems

Parallel Direct and Iterative Methods for Solving the Time-Fractional Diffusion Equation on Multicore Processors

Second Refinement of Accelerated over Relaxation Method for the Solution of Linear System

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