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Volume 35, Issue 2
Asymptotic Eigenvalue Estimation for a Class of Structured Matrices

Juan Liang, Jiangzhou Lai & Qiang Niu

Ann. Appl. Math., 35 (2019), pp. 152-158.

Published online: 2020-08

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  • Abstract

In this paper we consider eigenvalue asymptotic estimations for a class of structured matrices arising from statistical applications. The asymptotic upper bounds of the largest eigenvalue ($λ$max) and the sum of squares of eigenvalues $(\sum\limits_{i=1}^nλ_i^2)$ are derived. Both these bounds are useful in examining the stability of certain Markov process. Numerical examples are provided to illustrate tightness of the bounds.

  • Keywords

Toeplitz matrix, eigenvalue, rank-one modification, trace.

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COPYRIGHT: © Global Science Press

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@Article{AAM-35-152, author = {Liang , JuanLai , Jiangzhou and Niu , Qiang}, title = {Asymptotic Eigenvalue Estimation for a Class of Structured Matrices}, journal = {Annals of Applied Mathematics}, year = {2020}, volume = {35}, number = {2}, pages = {152--158}, abstract = {

In this paper we consider eigenvalue asymptotic estimations for a class of structured matrices arising from statistical applications. The asymptotic upper bounds of the largest eigenvalue ($λ$max) and the sum of squares of eigenvalues $(\sum\limits_{i=1}^nλ_i^2)$ are derived. Both these bounds are useful in examining the stability of certain Markov process. Numerical examples are provided to illustrate tightness of the bounds.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18074.html} }
TY - JOUR T1 - Asymptotic Eigenvalue Estimation for a Class of Structured Matrices AU - Liang , Juan AU - Lai , Jiangzhou AU - Niu , Qiang JO - Annals of Applied Mathematics VL - 2 SP - 152 EP - 158 PY - 2020 DA - 2020/08 SN - 35 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/18074.html KW - Toeplitz matrix, eigenvalue, rank-one modification, trace. AB -

In this paper we consider eigenvalue asymptotic estimations for a class of structured matrices arising from statistical applications. The asymptotic upper bounds of the largest eigenvalue ($λ$max) and the sum of squares of eigenvalues $(\sum\limits_{i=1}^nλ_i^2)$ are derived. Both these bounds are useful in examining the stability of certain Markov process. Numerical examples are provided to illustrate tightness of the bounds.

Juan Liang, Jiangzhou Lai & Qiang Niu. (2020). Asymptotic Eigenvalue Estimation for a Class of Structured Matrices. Annals of Applied Mathematics. 35 (2). 152-158. doi:
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