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2013•Unpublished venueRequires access

Preconditioned AOR Iterative Method for M-Matrix

Qiufang Xue, Xingbao Gao, Xiaoguang Liu

Open publisher page 1 citations

Abstract

In this paper, we propose a new selection mode of 'r, t' for the preconditioner I+C and analyze the convergence performance of the preconditioned AOR iterative method induced by this preconditioner. For a nonsingular M-matrix, we show that the preconditioned AOR iterative method with this choice and the preconditioned methods advised by Evans et al. are all convergent, and that the preconditioned method with the preconditioner I+C has faster convergence speed than the original AOR method. Finally, the limit numerical results are provided to support the obtained results.

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What this paper is about

In this paper, we propose a new selection mode of 'r, t' for the preconditioner I+C and analyze the convergence performance of the preconditioned AOR iterative method induced by this preconditioner. For a nonsingular M-matrix, we show that the preconditioned AOR iterative method with this choice and the preconditioned methods advised by Evans et al. are all convergent, and that the preconditioned method with the preconditioner I+C has faster convergence speed than the original AOR method. Finally, the limit numerical results are provided to support the obtained results.

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Available abstract

In this paper, we propose a new selection mode of 'r, t' for the preconditioner I+C and analyze the convergence performance of the preconditioned AOR iterative method induced by this preconditioner. For a nonsingular M-matrix, we show that the preconditioned AOR iterative method with this choice and the preconditioned methods advised by Evans et al. are all convergent, and that the preconditioned method with the preconditioner I+C has faster convergence speed than the original AOR method. Finally, the limit numerical results are provided to support the obtained results.

Key concepts: Preconditioner, Iterative method, Invertible matrix, Convergence (economics), Matrix (chemical analysis), Mathematics, Applied mathematics, Computer science

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