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| ASYMPTOTIC EIGENVALUE ESTIMATION FOR A CLASS OF STRUCTURED MATRICES |
| Juan Liang,Jiangzhou Lai,Qiang Niu |
| (School of Math. and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, PR China;School of Math. and Computer Science, Fuzhou University, Fuzhou 350108, Fujian, PR China;Dept. of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou 215123, Jiangsu, PR China) |
| DOI： |
| 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 (\lambda_{\max}) and the sum of squares of eigenvalues \Big(\sums_{i=1}^n\lambda_i^2\Big) 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. |
| Key words: Toeplitz matrix; eigenvalue; rank-one modification; trace |