• ISSN 1006-3080
• CN 31-1691/TQ

 引用本文: 吴思婷, 鲍亮, 黄景宣. 求解正定线性方程组的外推的PSS迭代方法[J]. 华东理工大学学报（自然科学版）.
WU Siting, BAO Liang, HUANG Jingxuan. An Extrapolated PSS Iterative Method for Positive Definite Linear Systems[J]. Journal of East China University of Science and Technology. doi: 10.14135/j.cnki.1006-3080.20210312001
 Citation: WU Siting, BAO Liang, HUANG Jingxuan. An Extrapolated PSS Iterative Method for Positive Definite Linear Systems[J]. Journal of East China University of Science and Technology.

## 求解正定线性方程组的外推的PSS迭代方法

##### doi: 10.14135/j.cnki.1006-3080.20210312001

###### 通讯作者: 鲍　亮，E-mail：lbao@ecust.edu.cn
• 中图分类号: O241.6

## An Extrapolated PSS Iterative Method for Positive Definite Linear Systems

• 摘要: 为了更高效地求解大型稀疏正定线性方程组，提出了一种外推的正定和反Hermitian迭代方法。新方法首先对系数矩阵进行正定和反Hermitian分裂(PSS)，再构造出了一种新的非对称二步迭代格式。同时理论分析了新方法的收敛性，并给出了新方法收敛的充要条件。数值实验表明，通过参数值的选择，新方法比PSS迭代方法和外推的Hermitian和反Hermitian分裂（EHSS）迭代方法具有更快的收敛速度和更小的迭代次数，选择合适的参数值时新方法的收敛效率可以大大提高。

• 图  1  例1中EPSS和PSS迭代方法的残量下降速度比较

Figure  1.  Comparison of the residuals speed in EPSS and PSS for example 1

图  2  例2取不同矩阵规模时，EPSS、PSS和EHSS迭代方法的残量下降速度比较

Figure  2.  Comparison of the residuals speed in EPSS, PSS and EHSS for example 2 when matrix size is different

图  3  例1取不同$qh$和最优ω时，EPSS和PSS迭代方法的谱半径与α的关系

Figure  3.  Relationship between the parameter α and the spectral radius in EPSS and PSS for example 1 when $qh$ is differert and ω is optimal

图  4  例1取不同$qh$时，EPSS迭代方法中参数$\alpha$$\omega$与谱半径的关系

Figure  4.  Relationship between the parameters $\alpha$,$\omega$ and the spectral radius in the EGHSS iterative method for example 1 when $qh$ is different

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##### 出版历程
• 收稿日期:  2021-03-12
• 网络出版日期:  2021-06-29

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