Iterative solution methods
Accelerated iterative method for Z-matrices
Journal of Computational and Applied Mathematics
A Generalized SOR Method for Dense Linear Systems of Boundary Element Equations
SIAM Journal on Scientific Computing
An iterative test for H-matrix
Journal of Computational and Applied Mathematics - Proceedings of the 8th international congress on computational and applied mathematics
A comparison theorem for the iterative method with the preconditioner (I + Smax)
Journal of Computational and Applied Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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
The preconditioned Gauss-Seidel method faster than the SOR method
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix @W in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum @W. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner P"G is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner P"G(@c"o"p"t) produces an extremely small spectral radius in comparison with the other schemes considered.