非Hermitian正定线性方程组的外推的HSS迭代方法  

ON EXTRAPOLATED HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHOD FOR NON-HERMITIAN POSITIVE DEFINITE LINEAR SYSTEMS

作　　者：潘春平[1] 王红玉[1] 曹文方[1] Pan Chunping;Wang Hongyu;Cao Wenfang(Dept.of Humanities and Social Sciences, Zhejiang Industry Polytechnic College, Shaoxing 312000, China)

机构地区：[1]浙江工业职业技术学院人文社科部,绍兴312000

出　　处：《计算数学》2019年第1期52-65,共14页Mathematica Numerica Sinica

基　　金：浙江省教育厅高校访问学者教师专业发展项目资助(FX2017116)

摘　　要：为了高效地求解大型稀疏非Hermitian正定线性方程组,在白中治、Golub和Ng提出的Hermitian和反Hermitian分裂(HSS)迭代法的基础上,通过引入新的参数并结合迭代法的松弛技术,对HSS迭代方法进行加速,提出了一种新的外推的HSS迭代方法(EHSS),并研究了该方法的收敛性.数值例子表明:通过参数值的选择,新方法比HSS方法具有更快的收敛速度和更少的迭代次数,选择了合适的参数值后,可以提高HSS方法的收敛效率.In order to solve large sparse non-Hermitian positive definite linear systems quickly and efficiently, Bai, Golub and Ng studied the Hermitian and skew-Hermitian splitting iterations(HSS). Through accelerating the HSS iterative algorithms by using new relaxation parameter, An extrapolated method of the Hermitian and skew-Hermitian splitting iterations(EHSS) is proposed in this paper. Under some suitable conditions, we give the convergence results. Numerical results show that the new method can improve the convergence efficiency, improve the HSS iterative methods.

关 键 词：迭代方法 交替迭代 HSS方法 非Hermitian矩阵 

分 类 号：O241.6[理学—计算数学]