求解一类特殊复对称线性方程组的尺度预处理迭代法  

Scaled Preconditioned Splitting Iterative Methods for Solving a Class of Complex Symmetric Linear Systems

作　　者：段永红[1] 温瑞萍[2] 高翔 DUAN Yonghong;WEN Ruiping;GAO Xiang(Department of Mathematics,Taiyuan Universitgu,Taiguan 030600,China;Key Laboratory for Engineering&Computing Science,Shanai Provincial Department of Education,Tainuan Normal Universitg,Jinzhong 030619,China)

机构地区：[1]太原学院数学系,山西太原030600 [2]太原师范学院工程科学计算山西省高等学校重点实验室,山西晋中030619

出　　处：《应用数学》2021年第3期665-673,共9页Mathematica Applicata

基　　金：Supported by the NSF of Shanxi Province (201901D211423);the STIP of Shanxi Provincial Department of Education (2020L0719);the CSREP in Shanxi (2019KJ035)。

摘　　要：针对一类特殊的复对称但非Hermitian线性方程组,本文提出两个尺度预处理迭代法.对新迭代方法的最优参数及谱半径性质进行详细的讨论.基于这些结果,在合理的条件下,证明新方法是收敛的.最后,通过数值实验验证了新方法的可行性和有效性.This paper constructs two scaled preconditioned splitting iterative methods for solving the system of linear equations when the coefficient matrix is a non-Hermitian but symmetric complex matrix.The formula of the optimal parameters and the spectral radius properties of the iteration matrix for the new methods are discussed in detail.Theoretical analyses show that the new methods are convergent under the reasonable conditions.Finally,the numerical experiments show the new methods to be feasible and effective.

关 键 词：复对称矩阵 分裂迭代法 收敛性 预处理 

分 类 号：O241.6[理学—计算数学]