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(λmax) and the sum of squares of eigenvalues(■)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.
Annals of Applied Mathematics
Juan Liang’s work was supported by Young and middle-aged teachers education research project of Fujian Provincial Education Department No.JT180300
Jiangzhou Lai’s work was supported by Core Courses for undergraduate majors of Fuzhou university No.0360-52000732
Qiang Niu’s work was supported by XJTLU research enhancement fund No.REF-18-01-04 and the XJTLU Key Programme Special Fund(KSF).