Iterative Approximation of Analytic Eigenvalues of a Parahermitian Matrix EVD

机译：帕尔米特矩阵EVD的解析特征值的迭代逼近

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We present an algorithm that extracts analytic eigenvalues from a parahermitian matrix. Operating in the discrete Fourier transform domain, an inner iteration re-establishes the lost association between bins via a maximum likelihood sequence detection driven by a smoothness criterion. An outer iteration continues until a desired accuracy for the approximation of the extracted eigenvalues has been achieved. The approach is compared to existing algorithms.

机译：我们提出了一种算法，该算法从准herheritian矩阵中提取解析特征值。在离散傅立叶变换域中操作，内部迭代通过由平滑度准则驱动的最大似然序列检测，重新建立仓之间的丢失关联。外部迭代将继续进行，直到达到所提取特征值近似值的所需精度为止。该方法与现有算法进行了比较。

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《IEEE International Conference on Acoustics, Speech and Signal Processing》|2019年|8038-8042|共5页
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Stephan Weiss; Ian K. Proudler; Fraser K. Coutts; Jennifer Pestana;
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Discrete Fourier transforms; Eigenvalues and eigenfunctions; Matrices; Covariance matrices; Time-domain analysis; Signal processing algorithms; Measurement;

机译：离散傅里叶变换;特征值和特征函数;矩阵;协方差矩阵;时域分析;信号处理算法;测量;

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专利

1. Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices [J] . Redif S., Weiss S., McWhirter J.G. Signal Processing, IEEE Transactions on . 2015,第1期

机译：准父矩阵多项式EVD的顺序矩阵对角化算法。
2. Corrections to “On the Existence and Uniqueness of the Eigenvalue Decomposition of a Parahermitian Matrix” [May 18 2659-2672] [J] . Stephan Weiss, Jennifer Pestana, Ian K. Proudler, IEEE Transactions on Signal Processing . 2018,第23期

机译：对“关于一个准herheritian矩阵的特征值分解的存在和唯一性”的更正[2年5月18日，2659-2672]
3. Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix [J] . Vlok J.D., Olivier J.C. Communications, IET . 2012,第12期

机译：白色Wishart矩阵的最大特征值分布的解析近似
4. Iterative Approximation of Analytic Eigenvalues of a Parahermitian Matrix EVD [C] . Stephan Weiss, Ian K. Proudler, Fraser K. Coutts, IEEE International Conference on Acoustics, Speech and Signal Processing . 2019

机译：参加者矩阵EVD分析特征值的迭代近似
5. Preconditioned iterative methods for linear systems, eigenvalue and singular value problems. [D] . Vecharynski, Eugene. 2011

机译：线性系统，特征值和奇异值问题的预处理迭代方法。
6. Rayleigh-Ritz and A. Weinstein Methods for Approximation of Eigenvalues [O] . N. Aronszajn 1948

机译：特征值近似的Rayleigh-Ritz和A.Weinstein方法
7. Iterative Approximation of Analytic Eigenvalues of a Parahermitian Matrix EVD [O] . Stephan Weiss, Ian K. Proudler, Fraser K. Coutts, 2019

机译：参加者矩阵EVD分析特征值的迭代近似
8. Application of vector-valued rational approximations to the matrix eigenvalue problem and connections with Krylov subspace methods [R] . Sidi, Avram 1992

机译：向量值有理逼近在矩阵特征值问题中的应用及与Krylov子空间方法的联系

Iterative Approximation of Analytic Eigenvalues of a Parahermitian Matrix EVD

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