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Volume 5, Issue 2
An Estimate of the Difference Between a Diagonal Element and the Corresponding Eigenvalue of a Symmetric Tridiagonal Matrix

Er-Xiong Jiang

J. Comp. Math., 5 (1987), pp. 144-155.

Published online: 1987-05

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  • Abstract

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.

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@Article{JCM-5-144, author = {Er-Xiong Jiang}, title = {An Estimate of the Difference Between a Diagonal Element and the Corresponding Eigenvalue of a Symmetric Tridiagonal Matrix}, journal = {Journal of Computational Mathematics}, year = {1987}, volume = {5}, number = {2}, pages = {144--155}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9539.html} }
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 -

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.

Er-Xiong Jiang. (1987). An Estimate of the Difference Between a Diagonal Element and the Corresponding Eigenvalue of a Symmetric Tridiagonal Matrix. Journal of Computational Mathematics. 5 (2). 144-155. doi:
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