非埃尔米特正定线性系统的m步预处理的斜埃尔米特和反埃尔米特分裂方法（英文）  

On m-step preconditioned lopsided Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems

作　　者：陈芳[1] 谢冬秀[1] 李青[1] CHEN Fang;XIE Dongxiu;LI Qing(School of Applied Science,Beijing Information Science and Technology Beijing 100192,China)

机构地区：[1]北京信息科技大学理学院,北京100192

出　　处：《应用数学与计算数学学报》2018年第2期212-222,共11页Communication on Applied Mathematics and Computation

基　　金：Project supported by the National Natural Science Foundation of China(11501038)

摘　　要：进一步研究了非埃尔米特正定线性系统的斜埃尔米特和反埃尔米特迭代方法,并在预处理的斜埃尔米特和反埃尔米特迭代方法的基础上,引入了m步多项式预处理子,证明了预处理的斜埃尔米特和反埃尔米特迭代方法在一定条件下是收敛的,而且得到了预处理的斜埃尔米特和反埃尔米特迭代方法的收缩因子.通过数值例子说明,对于非埃尔米特正定线性系统m步的预处理有效地加速了Krylov子空间方法,例如GMRES.We further study the lopsided Hermitian and skew-Hermitian splitting（HSS） iteration method for solving non-Hermitian positive-definite linear systems.An m-step polynomial preconditioner based on the preconditioned lopsided HSS iteration method is introduced. The convergence of the preconditioned lopsided HSS iteration method is proved under weaker conditions. Moreover, the contraction factor of the preconditioned lopsided HSS method is derived. Numerical examples show that the m-step polynomial preconditioner is efficient in accelerating Krylov subspace methods, e.g., GMRES, for solving non-Hermitian positive-definite linear systems.

关 键 词：KRYLOV子空间方法 斜埃尔米特和反埃尔米特分裂方法 m步的多项式预处理 非埃尔米特正定线性系统 

分 类 号：O241.6[理学—计算数学]