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  • CN 31-1691/TQ

求解正定线性方程组的外推的PSS迭代方法

吴思婷 鲍亮 黄景宣

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

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
详细信息
    作者简介:

    吴思婷(1996-),女,浙江温州人,硕士生,主要研究方向:数值代数及其应用。E-mail:wusiting96@163.com

    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

    表  1  例1 PSS和EPSS迭代方法谱半径,收敛迭代次数和时间

    Table  1.   Spectral radius, IT and CPU of PSS and EPSS iterative method for example 1

    $qh$$N$PSSEPSS
    $\rho $ITCPU$\rho $ITCPU
    10 64 0.3583 36 0.0015 0.1973 23 0.0010
    128 0.4355 52 0.0027 0.2268 37 0.0016
    256 0.5623 73 0.0069 0.3782 47 0.0034
    512 0.6696 102 0.0443 0.4925 65 0.0081
    100 64 0.7094 100 0.0036 0.3084 14 0.0012
    128 0.7609 139 0.0053 0.3214 15 0.0017
    256 0.8126 193 0.0118 0.3238 19 0.0021
    512 0.8610 268 0.1010 0.3240 28 0.0051
    1000 64 0.7391 43 0.0057 0.1929 8 0.0010
    128 0.8182 68 0.0069 0.2153 10 0.0015
    256 0.9048 131 0.0221 0.2873 22 0.0019
    512 0.9512 276 0.1134 0.2968 15 0.0043
    下载: 导出CSV

    表  2  例2 PSS、EPSS和EHSS迭代方法谱半径,收敛迭代次数以及时间(q=1000)

    Table  2.   Spectral radius, IT and CPU of PSS, EPSS and EHSS iterative method for example 2 when $q = 1\;000$

    N$\omega $$\alpha $$\rho $ITCPU
    PSS83.50.5329220.0469
    102.90.5825250.1406
    122.60.6270300.4375
    142.30.6626330.9219
    EPSS80.13.90.5191210.0156
    100.13.30.5657240.0781
    120.12.90.6094270.3594
    140.12.60.6460310.7969
    EHSS80.13.30.6269330.0313
    100.12.50.6508330.1563
    120.12.20.6869370.4063
    140.14.30.6978381.0625
    下载: 导出CSV
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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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