An Estimate of the Difference Between a Diagonal Element and the Corresponding Eigenvalue of a Symmetric Tridiagonal Matrix

An Estimate of the Difference Between a Diagonal Element and the Corresponding Eigenvalue of a Symmetric Tridiagonal Matrix

Year:    1987

Journal of Computational Mathematics, Vol. 5 (1987), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1987-JCM-9539

Journal of Computational Mathematics, Vol. 5 (1987), Iss. 2 : pp. 144–155

Published online:    1987-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords: