Abstract
In this paper, the preconditioned accelerated overrelaxation (AOR) method for solving a class of two-by-two linear systems is presented. A new preconditioner is proposed according to the idea of [1] by Wu and Huang. The spectral radii of the iteration matrix of the preconditioned and the original methods are compared. The comparison results show that the convergence rate of the preconditioned AOR methods is indeed better than that of the original AOR methods, whenever the original AOR methods are convergent under certain conditions. Finally, a numerical example is presented to confirm our results.
Highlights
Sometimes we have to solve the following linear systems Hx f, (1.1) where H IB1 C is non-singular with D B2 B1 bij p p, B2 bij n p n p
A new preconditioner is proposed according to the idea of [1] by Wu and Huang
The comparison results show that the convergence rate of the preconditioned accelerated overrelaxation (AOR) methods is better than that of the original AOR methods, whenever the original AOR methods are convergent under certain conditions
Summary
The preconditioned accelerated overrelaxation (AOR) method for solving a class of two-by-two linear systems is presented. The spectral radii of the iteration matrix of the preconditioned and the original methods are compared. The linear systems (1.1) can be solved by direct methods or iterative methods.
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