A new iterative method for solving linear systems. (English) Zbl 1102.65039

Summary: A new iterative method for solving linear systems is derived. It can be considered as a modification of the Gauss-Seidel method. The modified method can be two times faster than the original one.


65F10 Iterative numerical methods for linear systems
Full Text: DOI


[1] Golub, G. H.; Van Loan, C. F., Matrix Computations (1996), The Johns Hopkins University Press: The Johns Hopkins University Press Baltimore and London · Zbl 0865.65009
[2] Hadjidimos, A., Successive overrelaxation (SOR) and related methods, J. Comput. Appl. Math., 123, 177-199 (2000) · Zbl 0965.65052
[3] Li, W., The convergence of the modified Gauss-Seidel methods for consistent linear systems, J. Comput. Appl. Math., 154, 97-105 (2003) · Zbl 1022.65034
[4] Li, W., A note on the preconditioned Gauss-Seidel (GS) method for linear systems, J. Comput. Appl. Math., 182, 81-90 (2005) · Zbl 1072.65042
[5] Li, W.; Sun, W., Modified Gauss-Seidel type methods and Jacobi type methods for \(Z\)-matrices, Lin. Alg. Appl., 317, 227-240 (2000) · Zbl 0966.65032
[6] Niki, H.; Harada, K.; Morimoto, M.; Sakakihara, M., The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method, J. Comput. Appl. Math., 164-165, 587-600 (2004) · Zbl 1057.65022
[7] Özban, A. Y., Improved convergence criteria for Jacobi and Gauss-Seidel iterations, Appl. Math. Comput., 152, 3, 693-700 (2004) · Zbl 1077.65033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.