Evans, D. J.; Martins, M. M.; Trigo, M. E. The AOR iterative method for new preconditioned linear systems. (English) Zbl 0992.65022 J. Comput. Appl. Math. 132, No. 2, 461-466 (2001). This paper deals with the accelerated over-relaxation (AOR) iterative method. It is proved that, under certain assumptions, the rate of convergence of the AOR iterative method can be enlarged if this method is applied to some new preconditioned linear systems. The results are illustrated by a numerical example. Reviewer: Liu Xinguo (Qingdao) Cited in 4 ReviewsCited in 25 Documents MSC: 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling Keywords:AOR method; preconditioning; accelerated over-relaxation iterative method; convergence; numerical example PDFBibTeX XMLCite \textit{D. J. Evans} et al., J. Comput. Appl. Math. 132, No. 2, 461--466 (2001; Zbl 0992.65022) Full Text: DOI References: [1] Evans, D. J.; Martins, M. M., The AOR method for \(AX − XB = C\), Internat. J. Comput. Math., 52, 75-82 (1994) [2] Evans, D. J.; Martins, M. M., The AOR method for preconditioned linear systems, Internat. J. Comput. Math., 5, 69-76 (1995) · Zbl 0847.65013 [3] Gunawardena, A. D.; Jain, S. K.; Snyder, L., Modified iterative methods for consistent linear systems, Linear Algebra Appl., 154-156, 123-143 (1991) · Zbl 0731.65016 [4] Hadjidimos, A., Accelerated overrelaxation method, Math. Comput., 32, 149-157 (1978) · Zbl 0382.65015 [5] C. Li, D.J. Evans, Improving the SOR method, Technical Report 901, Department of Computer Studies, University of Loughborough, 1994.; C. Li, D.J. Evans, Improving the SOR method, Technical Report 901, Department of Computer Studies, University of Loughborough, 1994. · Zbl 0828.65030 [6] Varga, R. S., Matrix Iterative Analysis (1981), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0133.08602 [7] Young, D. M., Iterative Solution of Large Linear Systems (1971), Academic Press: Academic Press New York · Zbl 0204.48102 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.