On the rate of convergence of the preconditioned conjugate gradient method
Numerische Mathematik
Topics in matrix analysis
Journal of the ACM (JACM)
A comparison theorem for the iterative method with the preconditioner (I + Smax)
Journal of Computational and Applied Mathematics
Block Gauss elimination followed by a classical iterative method for the solution of linear systems
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)
Comparison results for solving preconditioned linear systems
Journal of Computational and Applied Mathematics
Comparison results on preconditioned SOR-type iterative method for Z-matrices linear systems
Journal of Computational and Applied Mathematics
The preconditioned Gauss-Seidel method faster than the SOR method
Journal of Computational and Applied Mathematics
Convergence analysis of the preconditioned Gauss-Seidel method for H-matrices
Computers & Mathematics with Applications
Some preconditioning techniques for linear systems
WSEAS Transactions on Mathematics
On the improved Gauss-Seidel method for linear systems
CISST'09 Proceedings of the 3rd WSEAS international conference on Circuits, systems, signal and telecommunications
An extended GS method for dense linear systems
Journal of Computational and Applied Mathematics
Study on the preconditioners (I+Sm)
Journal of Computational and Applied Mathematics
Hi-index | 7.30 |
Many researchers have considered preconditioners, applied to linear systems, whose matrix coefficient is a Z-or an M-matrix, that make the associated Jacobi and Gauss-Seidel methods converge asymptotically faster than the unpreconditioned ones. Such preconditioners are chosen so that they eliminate the off-diagonal elements of the same column or the elements of the first upper diagonal [Milaszewicz, LAA 93 (1987) 161-170], Gunawardena et al. [LAA 154-156 (1991) 123-143]. In this work we generalize the previous preconditioners to obtain optimal methods. "Good" Jacobi and Gauss-Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are also proposed and analyzed. Moreover, the behavior of the above preconditioners to the Krylov subspace methods is studied.