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Modified iterative methods for consistent linear systems. (English) Zbl 0731.65016

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)

MSC:

65F10 Iterative numerical methods for linear systems
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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
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