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Abstract: . The classical perturbation theory for Hermitian 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... (Update)
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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/li98relative.html More
@article{ li98relative,
author = "Ren-Cang Li",
title = "Relative Perturbation Theory: {I}. Eigenvalue and Singular Value Variations",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "19",
number = "4",
pages = "956--982",
year = "1998",
url = "citeseer.ist.psu.edu/article/li98relative.html" }
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[Article contains additional citations not shown here]
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