Block Gauss elimination followed by a classical iterative method for the solution of linear systems
Journal of Computational and Applied Mathematics
On optimal improvements of classical iterative schemes for Z-matrices
Journal of Computational and Applied Mathematics
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
On optimal improvements of classical iterative schemes for Z-matrices
Journal of Computational and Applied Mathematics
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Occasionally in the numerical solution of elliptic partial differential equations the rate of convergence of relaxation methods to the solution is adversely affected by the relative proximity of certain points in the grid. It has been proposed that the removal of the unknown functional values at these points by Gaussian elimination may accelerate the convergence.By application of the Perron-Frobenius theory of non-negative matrices it is shown that the rates of convergence of the Jacobi-Richardson and Gauss-Seidel iterations are not decreased and could be increased by this elimination. Although this may indicate that the elimination could improve the convergence rate for overrelaxation, it is still strictly an unsolved problem.