Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 218, Issue 2, Pages 260-270Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.05.036
Keywords
Chebyshev's method; Approximate inverse preconditioner; Convergent
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Funding
- NSFC [11026085, 60973015, 60973151]
- 973 Program [2007CB311002]
- Sichuan Province Sci. & Tech. Research Project [2011JY0002, 2009SPT-1, 2009GZ0004, 2009HH0025]
- Fundamental Research Funds for the Central Universities [ZYGX2009J103]
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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. (C) 2011 Elsevier Inc. All rights reserved.
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