ON STRUCTURED VARIANTS OF MODIFIED HSS ITERATION METHODS FOR COMPLEX TOEPLITZ LINEAR SYSTEMS  

作　　者：Fang Chen Yaolin Jiang Qingquan Liu 

机构地区：[1]Department of Mathematical Sciences, Xi'an Jiaotong University, Xi'an 710049, China [2]Key Laboratory of Environmental Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Journal of Computational Mathematics》2013年第1期57-67,共11页计算数学（英文）

基　　金：Acknowledgments. The work was supported by State Key Laboratory of Scientific/Engineer- ing Computing, Chinese Academy of Sciences; The International Science and Technology Co- operation Program of China under Grant 2010DFA14700; The Natural Science Foundation of China （NSFC） under Grant 11071192, P.R. China.

摘　　要：The Modified Hermitian and skew-Hermitian splitting （MHSS） iteration method was presented and studied by Bai, Benzi and Chen （Computing, 87（2010）, 93-111） for solving a class of complex symmetric linear systems. In this paper, using the properties of Toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex Toeplitz linear system. Theoretical analysis shows that the structured MHSS iteration method is unconditionally convergent to the exact solution. When the MHSS iteration method is used directly to complex symmetric Toeplitz linear systems, the computational costs can be considerately reduced by use of Toeplitz structure. Finally, numerical ex- periments show that the structured MHSS iteration method and the structured MHSS preconditioner are efficient for solving the complex Toeplitz linear system.The Modified Hermitian and skew-Hermitian splitting （MHSS） iteration method was presented and studied by Bai, Benzi and Chen （Computing, 87（2010）, 93-111） for solving a class of complex symmetric linear systems. In this paper, using the properties of Toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex Toeplitz linear system. Theoretical analysis shows that the structured MHSS iteration method is unconditionally convergent to the exact solution. When the MHSS iteration method is used directly to complex symmetric Toeplitz linear systems, the computational costs can be considerately reduced by use of Toeplitz structure. Finally, numerical ex- periments show that the structured MHSS iteration method and the structured MHSS preconditioner are efficient for solving the complex Toeplitz linear system.

关 键 词：Toeplitz matrix MHSS iteration method Complex symmetric linear system. 

分 类 号：O241.6[理学—计算数学] TQ464.54[理学—数学]