Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices
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- by Zhong-Zhi Bai, Gene H. Golub and Chi-Kwong Li PDF
- Math. Comp. 76 (2007), 287-298 Request permission
Abstract:
For the non-Hermitian and positive semidefinite systems of linear equations, we derive necessary and sufficient conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. We then apply these results to block tridiagonal linear systems in order to obtain convergence conditions for the corresponding block variants of the preconditioned Hermitian and skew-Hermitian splitting iteration methods.References
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Additional Information
- Zhong-Zhi Bai
- Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China, and State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People’s Republic of China
- Email: bzz@lsec.cc.ac.cn
- Gene H. Golub
- Affiliation: Scientific Computing and Computational Mathematics Program, Department of Computer Science, Stanford University, Stanford, California 94305-9025
- Email: golub@sccm.stanford.edu
- Chi-Kwong Li
- Affiliation: Department of Mathematics, The College of William & Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
- MR Author ID: 214513
- Email: ckli@math.wm.edu
- Received by editor(s): February 11, 2005
- Published electronically: August 31, 2006
- Additional Notes: The work of the first author was supported by The Special Funds For Major State Basic Research Projects (No. G1999032803), The National Basic Research Program (No. 2005CB321702), The China NNSF Outstanding Young Scientist Foundation (No. 10525102) and The National Natural Science Foundation (No. 10471146), P.R. China, and The 2004 Ky and Yu-Fen Fan Fund Travel Grant of American Mathematical Society
The work of the second author was in part supported by the Department of Energy: DE-FC02-01ER41177
The research of the third author was partially supported by an NSF grant. - © Copyright 2006 American Mathematical Society
- Journal: Math. Comp. 76 (2007), 287-298
- MSC (2000): Primary 65F10, 65F50
- DOI: https://doi.org/10.1090/S0025-5718-06-01892-8
- MathSciNet review: 2261022