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基于加权矩阵的多维广义特征值并行分解算法

高迎彬 徐中英

高迎彬, 徐中英. 基于加权矩阵的多维广义特征值并行分解算法. 自动化学报, 2020, 41(x): 1−7 doi: 10.16383/j.aas.c200399
引用本文: 高迎彬, 徐中英. 基于加权矩阵的多维广义特征值并行分解算法. 自动化学报, 2020, 41(x): 1−7 doi: 10.16383/j.aas.c200399
Gao Ying-Bin, Xu Zhong-Ying. Multiple generalized eigenvalue decomposition algorithm in parallel based on weighted matrix. Acta Automatica Sinica, 2020, 41(x): 1−7 doi: 10.16383/j.aas.c200399
Citation: Gao Ying-Bin, Xu Zhong-Ying. Multiple generalized eigenvalue decomposition algorithm in parallel based on weighted matrix. Acta Automatica Sinica, 2020, 41(x): 1−7 doi: 10.16383/j.aas.c200399

基于加权矩阵的多维广义特征值并行分解算法

doi: 10.16383/j.aas.c200399
基金项目: 国家自然科学基金(61673387, 61903375)资助
详细信息
    作者简介:

    高迎彬:中国电子科技集团公司第五十四研究所工程师, 主要研究方向为自适应信号处理和神经网络等

    徐中英 火箭军工程大学副教授, 主要研究方向为统计信号处理和系统建模等. 本文通信作者: E-mail: xuzhy1978@163.com

Multiple Generalized Eigenvalue Decomposition Algorithm in Parallel Based on Weighted Matrix

Funds: Supported by National Natural Science Foundation of P. R. China (61673387, 61903375)
  • 摘要: 针对串行广义特征值分解算法实时性差的缺点, 提出了基于加权矩阵的多维广义特征值分解算法. 与串行算法不同, 所提算法能够在一次迭代过程中并行地估计出多维广义特征向量. 平稳点分析表明: 当且仅当算法中状态矩阵等于所需的广义特征向量时, 算法达到收敛状态. 通过对比相邻时刻的状态矩阵模值证明了所提算法的自稳定特性. 所提算法参数选取简单, 实际实施较为容易. 数值仿真和实例应用进一步验证了算法的并行性、自稳定性和实用性.
  • 图  1  所提算法方向余弦曲线

    Fig.  1  The DC curves of the proposed algorithm

    图  2  GDM算法方向余弦曲线

    Fig.  2  The DC curves of the GDM algorithm

    图  3  列向量模值曲线

    Fig.  3  The norm curves of the column vectors

    图  4  不同列向量内积关系曲线

    Fig.  4  The inner product curves of different column vectors

    图  5  不同对角矩阵下状态矩阵模值曲线

    Fig.  5  The norm curves of the state matrix with different diagonal matrices

    图  6  源信号波形

    Fig.  6  The waveform of source signals

    图  7  观测信号曲线

    Fig.  7  The waveform of observed signals

    图  8  分离信号曲线

    Fig.  8  The waveform of separated signals

    表  1  两种算法的计算时间

    Table  1  The time cost of the two algorithms

    算法所提算法GDM算法
    时间2.16 ms14.61 ms
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-06-10
  • 修回日期:  2020-09-26
  • 网络出版日期:  2020-12-17

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