TY - JOUR
T1 - An Estimate of the Difference Between a Diagonal Element and the Corresponding Eigenvalue of a Symmetric Tridiagonal Matrix
AU - Er-Xiong Jiang
JO - Journal of Computational Mathematics
VL - 2
SP - 144
EP - 155
PY - 1987
DA - 1987/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9539.html
KW - 
AB - <p style="text-align: justify;">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 $\beta_1$ is replaced by zero and when two neighboring off-diagonal elements $ \beta_{i-1},\beta_i$ are replaced by zero.</p>