### Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion

Elsner L, He C, Mehrmann V (1995)
Numerical Linear Algebra with Applications 2(2): 155-171.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Elsner, LudwigUniBi; He, Chunyang; Mehrmann, Volker
Einrichtung
Abstract / Bemerkung
We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.
Stichworte
CONDITION NUMBER; MATRIX COMPLETION; DILATION THEORY; ROBUST REGULARIZATION OF DESCRIPTOR SYSTEMS; NORM OF A MATRIX
Erscheinungsjahr
1995
Zeitschriftentitel
Numerical Linear Algebra with Applications
Band
2
Ausgabe
2
Seite(n)
155-171
ISSN
1070-5325
Page URI
https://pub.uni-bielefeld.de/record/1640789

### Zitieren

Elsner L, He C, Mehrmann V. Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion. Numerical Linear Algebra with Applications. 1995;2(2):155-171.
Elsner, L., He, C., & Mehrmann, V. (1995). Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion. Numerical Linear Algebra with Applications, 2(2), 155-171. doi:10.1002/nla.1680020207
Elsner, L., He, C., and Mehrmann, V. (1995). Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion. Numerical Linear Algebra with Applications 2, 155-171.
Elsner, L., He, C., & Mehrmann, V., 1995. Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion. Numerical Linear Algebra with Applications, 2(2), p 155-171.
L. Elsner, C. He, and V. Mehrmann, “Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion”, Numerical Linear Algebra with Applications, vol. 2, 1995, pp. 155-171.
Elsner, L., He, C., Mehrmann, V.: Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion. Numerical Linear Algebra with Applications. 2, 155-171 (1995).
Elsner, Ludwig, He, Chunyang, and Mehrmann, Volker. “Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion”. Numerical Linear Algebra with Applications 2.2 (1995): 155-171.

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