A property of eigenvalue bounds for a class of symmetric tridiagonal interval matrices

Abstract

The eigenvalue bounds of interval matrices are often required in some mechanical and engineering fields. In this paper, we consider an interval eigenvalue problem with symmetric tridiagonal matrices. A theoretical result is obtained that under certain assumptions the upper and lower bounds of interval eigenvalues of the problem must be achieved just at some vertex matrices of the interval matrix. Then a sufficient condition is provided to guarantee the assumption to be satisfied. The conclusion is illustrated also by a numerical example.A k+1,nThe eigenvalues of W k are denoted and ordered as 1 2 ··· n−1 .