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Relative Perturbation Theory: (I) Eigenvalue and Singular Value Variations (1996)  (Make Corrections)  (4 citations)
Ren-Cang Li



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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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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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78   Computing accurate eigensystems of scaled diagonally dominan.. - Barlow, Demmel - 1990
18   Norms and exclusion theorems (context) - Bauer, Fike - 1960
15   Perturbation Bounds for Matrix Eigenvalues (context) - Bhatia - 1987

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