Modified Hermitian and skew‐Hermitian splitting methods for non‐Hermitian positive‐definite linear systems |
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| Authors: | Liang Li Ting‐Zhu Huang Xing‐Ping Liu |
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| Institution: | 1. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, People's Republic of China;2. School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, People's Republic of ChinaSchool of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, People's Republic of China===;3. State Key Lab of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, People's Republic of China |
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| Abstract: | To further study the Hermitian and non‐Hermitian splitting methods for a non‐Hermitian and positive‐definite matrix, we introduce a so‐called lopsided Hermitian and skew‐Hermitian splitting and then establish a class of lopsided Hermitian/skew‐Hermitian (LHSS) methods to solve the non‐Hermitian and positive‐definite systems of linear equations. These methods include a two‐step LHSS iteration and its inexact version, the inexact Hermitian/skew‐Hermitian (ILHSS) iteration, which employs some Krylov subspace methods as its inner process. We theoretically prove that the LHSS method converges to the unique solution of the linear system for a loose restriction on the parameter α. Moreover, the contraction factor of the LHSS iteration is derived. The presented numerical examples illustrate the effectiveness of both LHSS and ILHSS iterations. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | non‐Hermitian positive‐definite matrix skew‐Hermitian matrix splitting iteration |
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