On performance of SOR method for solving nonsymmetric linear systems

• Published in: Journal of computational and applied mathematics Vol. 137; no. 1; pp. 145 - 176
• Main Author: WOZNICKI, Zbigniew I
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2001; Elsevier
• Subjects: Difference approximation; Exact sciences and technology; Linear equation systems; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Point and line SOR algorithms; Sciences and techniques of general use; Sparse matrices; Symmetric and nonsymmetric matrices; Sparse matrices; Difference approximation; Point and line SOR algorithms; Linear equation systems; Symmetric and nonsymmetric matrices; Solution uniqueness; Non symmetric matrix; Iterative method; Non singular matrix; Algorithm; Partial differential equation; Convergence; Equation system; Linear system; Linear equation; Symmetric matrix; Overrelaxation method; Finite difference method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(00)00705-6

The main subject of the paper is the study of the performance of SOR algorithms for solving linear systems of the type arising from the difference approximation of nonself-adjoint two-dimensional elliptic partial differential equations. A special attention is paid to the development of efficient techniques for determining the optimum relaxation parameter providing the maximum rate of convergence. Four models of the behaviour of the spectral radius of the SOR matrix as a function of relaxation parameter are analyzed. Numerical experiments are performed for several problems with nonsymmetric coefficient matrices taken from the literature. A comparison of results of the line-SOR method with the results obtained from different GMRES algorithms shows that with the computational work comparable for both methods, the line-SOR method provides the solutions of considered problems with the second norm of the error vector a few orders lesser in the magnitude.