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

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.