Abstract
The relative error in \(\hat{\alpha}=\alpha(1+\delta)\) as an approximation to α is measured by
In terms of this measurement we give a Hoffman–Wielandt type bound of singular values under additive perturbations and a Bauer–Fike type bound of eigenvalues under multiplicative perturbations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Demmel and K. Veselic, Jacobi’s method is more accurate than QR, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 195–234.
S. Eisenstat and I. C. F. Ipsen, Relative Perturbation Results for Eigenvalues and Eigenvectors of Diagonalisable Matrices, Technical Report CRSC-TR96-6, Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, 1996.
I. C. F. Ipsen, Relative perturbation results for matrix eigenvalues and singular values, Acta Numerica, 7 (1998), pp. 151–201.
R. C. Li, Bounds on perturbations of generalized singular values and of associated subspaces, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 195–234.
R. C. Li, Relative perturbation theory: I. Eigenvalue and singular value variations, SIAM J. Matrix Anal. Appl., 19 (1998), pp. 956–982.
R. C. Li, Relative perturbation theory: III. More bounds on eigenvalue variation, Linear Algebra Appl., 266 (1997), pp. 337–345.
Author information
Authors and Affiliations
Corresponding author
Additional information
AMS subject classification (2000)
65F15, 15A18
Rights and permissions
About this article
Cite this article
Chen, X. Two perturbation bounds for singular values and eigenvalues . Bit Numer Math 48, 493–497 (2008). https://doi.org/10.1007/s10543-008-0187-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10543-008-0187-7