(untitled) (Journal of Computational Mathematics, 1987)
A sharper upperbound of the difference between a diagonal element and the corresponding eigenvalue of a symmetric tridiagonal matrix is given. The bound can be used in QL and QR algorithms and Rayleigh quotient approximation. The change of eigenvalues is estimated when the first off-diagonal element β_1 is replaced by zero and when two neighboring off-diagonal elements β_i-1,β_i are replaced by zero.