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A Feasible Approach to Determine the Optimal Relaxation Parameters in Each Iteration for the SOR Method

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  • Chein-Shan Liu

Abstract

The paper presents a dynamic and feasible approach to the successive over-relaxation (SOR) method for solving large scale linear system through iteration. Based on the maximal orthogonal projection technique, the optimal relaxation parameter is obtained by minimizing a derived merit function in terms of right-hand side vector, the coefficient matrix and the previous step values of unknown variables. At each iterative step, we can quickly determine the optimal relaxation value in a preferred interval. When the theoretical optimal value is hard to be achieved, the new method provides an alternative choice of the relaxation parameter at each iteration. Numerical examples confirm that the dynamic optimal successive over-relaxation (DOSOR) method outperforms the classical SOR method.

Suggested Citation

  • Chein-Shan Liu, 2021. "A Feasible Approach to Determine the Optimal Relaxation Parameters in Each Iteration for the SOR Method," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 13(1), pages 1-1, February.
    • Handle: RePEc:ibn:jmrjnl:v:13:y:2021:i:1:p:1
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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