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Abstract: The classical perturbation theory for matrix eigenvalue and singular value problems provides bounds on the absolute differences between approximate eigenvalues (singular values) and the true eigenvalues (singular values) of a matrix. These bounds may be bad news for small eigenvalues (singular values), which thereby suffer worse relative uncertainty than large ones. However, there are situations where even small eigenvalues are determined to high relative accuracy by the data, much more... (Update)
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...from L L t to D 1 LD 2 D 2 L t D 1 . Outer perturbations corresponding to D 1 have been studied by several authors, see [6] 7] [10], 11] 12] and [19] and cause small relative changes in each eigenvalue. A preliminary study of inner perturbations, corresponding to D...
...inner perturbation to N r D r N t r . Outer (multiplicative) perturbations have received considerable attention recently, see [9] 10] [18], 19] and [20] but the effect of inner perturbations is harder to assess. We reproduce here the simplest results on outer...
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BibTeX entry: (Update)
Ren-Cang Li, `Relative perturbation theory: (I) Eigenvalue and singular value variations'. SIAM J. Matrix Anal. Appl. vol. 19 (1998), pp. 956{ 982. http://citeseer.ist.psu.edu/article/li96relative.html More
@misc{ li98relative,
author = "R. Li",
title = "Relative perturbation theory: (I) Eigenvalue and singular value variations",
text = "Ren-Cang Li, `Relative perturbation theory: (I) Eigenvalue and singular
value variations'. SIAM J. Matrix Anal. Appl. vol. 19 (1998), pp. 956{ 982.",
year = "1998",
url = "citeseer.ist.psu.edu/article/li96relative.html" }
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18 Norms and exclusion theorems (context) - Bauer, Fike - 1960
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