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一类实矩阵对广义奇异值的表达公式

沈卫杰 汤天宇 徐玮玮

沈卫杰, 汤天宇, 徐玮玮. 一类实矩阵对广义奇异值的表达公式[J]. 华南师范大学学报(自然科学版), 2021, 53(6): 111-114. doi: 10.6054/j.jscnun.2021100
引用本文: 沈卫杰, 汤天宇, 徐玮玮. 一类实矩阵对广义奇异值的表达公式[J]. 华南师范大学学报(自然科学版), 2021, 53(6): 111-114. doi: 10.6054/j.jscnun.2021100
SHEN Weijie, TANG Tianyu, XU Weiwei. The Formula of Generalized Singular Values of a Class of Real Matrix Pairs[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(6): 111-114. doi: 10.6054/j.jscnun.2021100
Citation: SHEN Weijie, TANG Tianyu, XU Weiwei. The Formula of Generalized Singular Values of a Class of Real Matrix Pairs[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(6): 111-114. doi: 10.6054/j.jscnun.2021100

一类实矩阵对广义奇异值的表达公式

doi: 10.6054/j.jscnun.2021100
基金项目: 

国家自然科学基金项目 11971243

江苏省自然科学基金项目 BK20181405

详细信息
    通讯作者:

    徐玮玮, Email: 002415@nuist.edu.cn

  • 中图分类号: O241.6

The Formula of Generalized Singular Values of a Class of Real Matrix Pairs

  • 摘要: 应用双随机矩阵的性质, 首先得到了一类实对角矩阵迹函数优化问题的解析解, 再由该解析解得到了计算实矩阵对第i个广义奇异值的表达公式, 最后数值算例验证了结论的有效性.
  • 表  1  已知实矩阵对{A, B} 计算的αi2f(Qi)- f(Qi-1)

    Table  1.   The αi2 and f(Qi)- f(Qi-1) calculated by known real matrix pair {A, B}

    i αi αi2 f(Qi) f(Qi)-f(Qi-1)
    1 0.993 0.987 0.987 0.987
    2 0.877 0.770 1.756 0.770
    3 0.606 0.368 2.124 0.368
    4 0.149 0.022 2.146 0.022
    下载: 导出CSV

    表  2  广义奇异值{(αi, βi)}i=1n

    Table  2.   The generalized singular values {(αi, βi)}i=1n

    i αi βi i αi βi
    1 0.996 0.085 94 0.087 0.996
    2 0.988 0.156 95 0.051 0.999
    3 0.987 0.159 96 0.039 0.999
    4 0.970 0.244 97 0.030 1.000
    5 0.950 0.314 98 0.022 1.000
    6 0.947 0.322 99 0.021 1.000
    7 0.928 0.373 100 0.007 1.000
    下载: 导出CSV

    表  3  已知广义奇异值计算的αi2f(Qi)-f(Qi-1)

    Table  3.   The αi2 and f(Qi)-f(Qi-1) calculated with known generalized singular values

    i αi2 f(Qi) f(Qi)-f(Qi-1)
    1 0.993 0.993 0.993
    2 0.976 1.968 0.976
    3 0.975 2.943 0.975
    4 0.941 3.884 0.941
    5 0.902 4.785 0.902
    6 0.897 5.682 0.897
    7 0.861 6.543 0.861
    94 0.008 34.596 0.008
    95 0.003 34.599 0.003
    96 0.002 34.601 0.002
    97 0.001 34.602 0.001
    98 0.000 34.602 0.000
    99 0.000 34.602 0.000
    100 0.000 34.602 0.000
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-02
  • 网络出版日期:  2022-01-10
  • 刊出日期:  2021-12-25

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