Gunawardena, Ananda D.; Jain, Surender Kumar; Snyder, Larry Modified iterative methods for consistent linear systems. (English) Zbl 0731.65016 Linear Algebra Appl. 154-156, 123-143 (1991). Given an M-matrix A, certain elementary row operations are performed before applying the Gauss-Seidel or Jacobi iteration in order to solve \(Ax=b.\) The essential idea is to eliminate the entries in the upper part of the matrix next to the diagonal. In some examples the convergence rate is substantially reduced. {Reviewer’s remark: There may be a connection with the incomplete LU- decomposition which is known to lead often to better convergence.} Reviewer: D.Braess (Bochum) Cited in 8 ReviewsCited in 72 Documents MSC: 65F10 Iterative numerical methods for linear systems Keywords:Gauss-Seidel iteration; M-matrix; Jacobi iteration; convergence rate; incomplete LU-decomposition PDFBibTeX XMLCite \textit{A. D. Gunawardena} et al., Linear Algebra Appl. 154--156, 123--143 (1991; Zbl 0731.65016) Full Text: DOI References: [1] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1979), Academic · Zbl 0484.15016 [2] Milaszewicz, J. P., Improving Jacobi and Gauss-Seidel iterations, Linear Algebra Appl., 93, 161-170 (1987) · Zbl 0628.65022 [3] Mokari-Bolhassan, M. E.; Trick, T. N., A new iterative algorithm for the solutions of large scale systems, presented at 28th Midwest Symposium on Circuits and Systems Louisville (1985), Ky. [5] Schneider, H., Theorems on \(M\)-splitting of a singular \(M\)-matrix, Linear Algebra Appl., 58, 407-424 (1984) · Zbl 0561.65020 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.