Asymptotics of the Perron-Frobenius eigenvalue of nonnegative Hessenberg-Toeplitz matrices

Janssen A.J.E.M.

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Asymptotics of the Perron-Frobenius eigenvalue of nonnegative Hessenberg-Toeplitz matrices

机译：非负Hessenberg-Toeplitz矩阵的Perron-Frobenius特征值的渐近性

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Asymptotic results for the Perron-Frobenius eigenvalue of a nonnegative Hessenberg-Toeplitz matrix as the dimension of the matrix tends to infinity are given. The results are used and interpreted in terms of source entropies in the case where the Hessenberg-Toeplitz matrix arises as the transition matrix of a finite-state machine generating certain constrained sequences of +or-1's.

机译：给出了非负Hessenberg-Toeplitz矩阵的Perron-Frobenius特征值随矩阵维数趋于无穷大的渐近结果。在Hessenberg-Toeplitz矩阵作为产生某些约束序列+或-1的有限状态机的转换矩阵出现的情况下，将根据源熵来使用和解释结果。

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《IEEE Transactions on Information Theory》 |1989年第6期|P.1340-1344|共5页
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Janssen A.J.E.M.;
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中图分类无线电电子学、电信技术;
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1. Asymptotic properties of the QR factorization of banded Hessenberg-Toeplitz matrices [J] . Chang XW, Gander MJ, Karaa S Numerical linear algebra with applications . 2005,第7期

机译：带状Hessenberg-Toeplitz矩阵QR分解的渐近性质
2. On comparison of the Perron-Frobenius eigenvalues of two ML-matrices [J] . Lindqvist BH. Linear Algebra and its Applications . 2002,第0期

机译：关于两个ML矩阵的Perron-Frobenius特征值的比较
3. Estimations for spectral radius of nonnegative matrices and the smallest eigenvalue of M -matrices [J] . Te Wang, Hongbin Lv, Haifeng Sang Journal of inequalities and applications . 2014,第1期

机译：非负矩阵的谱半径估计和M矩阵的最小特征值
4. Monotonic Convergence to Eigenvalues of Totally Nonnegative Matrices in an Integrable Variant of the Discrete Lotka-Volterra System [C] . Akihiko Tobita, Akiko Fukuda, Emiko Ishiwata, International workshop on eigenvalue problems: algorithms, software and applications in petascale computing . 2017

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5. Characterizations of matrices enjoying the Perron-Frobenius property and generalizations of M-matrices which may not have nonnegative inverses. [D] . Elhashash, Abed. 2008

机译：享受Perron-Frobenius属性的矩阵的刻画以及可能没有非负逆的M矩阵的推广。
6. On the asymptotic eigenvalue distribution of a pseudo-differential operator [O] . C. Fefferman, D. H. Phong 1980

机译：伪微分算子的渐近特征值分布
7. On the Perron-Frobenius eigenvector for nonnegative integral matrices whose largest eigenvalue is integral [O] . Ashley Jonathan 1987

机译：关于最大特征值是积分的非负积分矩阵的Perron-Frobenius特征向量
8. Foundations of Eigenvalue Distribution Theory for General & Nonnegative Matrices, Stability Criteria for Hyperbolic Initial-Boundary Value Problems, Exact Eigenvalue Computations on the ILLIAC IV [R] . Marcus, M., Goldberg, M., Newman, M., 1980

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Asymptotics of the Perron-Frobenius eigenvalue of nonnegative Hessenberg-Toeplitz matrices

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