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 - <p style="text-align: justify;">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 ($λ$<sub>max</sub>) 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.</p>