The SOR and AOR Methods with Stepwise Optimized Values of Parameters for the Iterative Solutions of Linear Systems

Authors

  • Chein-Shan Liu Center of Excellence for Ocean Engineering, Center of Excellence for the Oceans, National Taiwan Ocean University, Keelung 202301, Taiwan
  • Chih-Wen Chang Department of Mechanical Engineering, National United University, Miaoli 360302, Taiwan https://orcid.org/0000-0001-9846-0694

DOI:

https://doi.org/10.37256/cm.5320245246

Keywords:

linear equations system, accelerated overrelaxation (AOR) method, modification of AOR (MAOR), step-by-step varying parameters, convergence

Abstract

We modify the successive overrelaxation (SOR) method and accelerated overrelaxation (AOR) method for solving linear equations systems. The optimal value of the acceleration parameter is determined, using the maximal reduction method of the residual vector’s length, or equivalently an orthogonality condition. Rather than the constant value, the MAOR method endows a step-by-step varying acceleration parameter to possess the property of absolute convergence and the orthogonality of consecutive residual vector. In SOR, the relaxation parameter is also optimized by using the orthogonality condition. Numerical examples ensure that the MSOR and MAOR iterative schemes converge faster than the original SOR and AOR iterative schemes. They are easily implemented with low computational cost, and without needing of a detailed spectral analysis to determine the optimal values of parameters has a great advantage.

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Published

2024-09-23

How to Cite

1.
Liu C-S, Chang C-W. The SOR and AOR Methods with Stepwise Optimized Values of Parameters for the Iterative Solutions of Linear Systems. Contemp. Math. [Internet]. 2024 Sep. 23 [cited 2024 Dec. 11];5(3):4013-28. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/5246