Chebyshev-type methods and preconditioning techniques |
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Authors: | Hou-Biao Li Ting-Zhu HuangYong Zhang Xing-Ping LiuTong-Xiang Gu |
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Affiliation: | a School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, PR China b Lab of Comp. Phys., Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China |
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Abstract: | Recently, a Newton’s iterative method is attracting more and more attention from various fields of science and engineering. This method is generally quadratically convergent. In this paper, some Chebyshev-type methods with the third order convergence are analyzed in detail and used to compute approximate inverse preconditioners for solving the linear system Ax = b. Theoretic analysis and numerical experiments show that Chebyshev’s method is more effective than Newton’s one in the case of constructing approximate inverse preconditioners. |
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Keywords: | Chebyshev&rsquo s method Approximate inverse preconditioner Convergent |
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