Asymptotic Eigenvalue Estimation for a Class of Structured Matrices

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.