Accelerated iterative method for Z-matrices
Journal of Computational and Applied Mathematics
A comparison theorem for the iterative method with the preconditioner (I + Smax)
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
On optimal improvements of classical iterative schemes for Z-matrices
Journal of Computational and Applied Mathematics
An extended GS method for dense linear systems
Journal of Computational and Applied Mathematics
Two new modified Gauss-Seidel methods for linear system with M-matrices
Journal of Computational and Applied Mathematics
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In recent years, a number of preconditioners have been applied to linear systems [A.D. Gunawardena, S.K. Jain, L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154-156 (1991) 123-143; T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123; H. Kotakemori, K. Harada, M. Morimoto, H. Niki, A comparison theorem for the iterative method with the preconditioner (I+S"m"a"x), J. Comput. Appl. Math. 145 (2002) 373-378; H. Kotakemori, H. Niki, N. Okamoto, Accelerated iteration method for Z-matrices, J. Comput. Appl. Math. 75 (1996) 87-97; M. Usui, H. Niki, T.Kohno, Adaptive Gauss-Seidel method for linear systems, Internat. J. Comput. Math. 51(1994)119-125 [10]]. Since these preconditioners are constructed from the elements of the upper triangular part of the coefficient matrix, the preconditioning effect is not observed on the nth row of matrix A. In the present paper, in order to deal with this drawback, we propose a new preconditioner. In addition, the convergence and comparison theorems of the proposed method are established. Simple numerical examples are also given, and we show that the convergence rate of the proposed method is better than that of the optimum SOR.