Minimizing the condition number of a positive definite matrix by completion

Elsner, Ludwig; He, Chunyang; Mehrmann, Volker

Minimizing the condition number of a positive definite matrix by completion

Elsner L, He C, Mehrmann V (1994)
Numerische Mathematik 69(1): 17-23.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Elsner_074.pdf

DOI

https://doi.org/10.1007/s002110050077

URN

urn:nbn:de:0070-pub-17749921

Autor*in

Elsner, Ludwig^UniBi; He, Chunyang; Mehrmann, Volker

Einrichtung

Fakultät für Mathematik

Abstract / Bemerkung

We consider the problem of minimizing the spectral condition number of a positive definite matrix by completion: [GRAPHICS] where A is an n x n Hermitian positive definite matrix, B a p x n matrix and X is a free p x p Hermitian matrix. We reduce this problem to an optimization problem for a convex function in one variable. Using the minimal solution of this problem we characterize the complete set of matrices that give the minimum condition number.

Erscheinungsjahr

1994

Zeitschriftentitel

Numerische Mathematik

Band

Ausgabe

Seite(n)

17-23

ISSN

0029-599X

eISSN

0945-3245

Page URI

https://pub.uni-bielefeld.de/record/1774992

Zitieren

Elsner L, He C, Mehrmann V. Minimizing the condition number of a positive definite matrix by completion. Numerische Mathematik. 1994;69(1):17-23.

Elsner, L., He, C., & Mehrmann, V. (1994). Minimizing the condition number of a positive definite matrix by completion. Numerische Mathematik, 69(1), 17-23. https://doi.org/10.1007/s002110050077

Elsner, Ludwig, He, Chunyang, and Mehrmann, Volker. 1994. “Minimizing the condition number of a positive definite matrix by completion”. Numerische Mathematik 69 (1): 17-23.

Elsner, L., He, C., and Mehrmann, V. (1994). Minimizing the condition number of a positive definite matrix by completion. Numerische Mathematik 69, 17-23.

Elsner, L., He, C., & Mehrmann, V., 1994. Minimizing the condition number of a positive definite matrix by completion. Numerische Mathematik, 69(1), p 17-23.

L. Elsner, C. He, and V. Mehrmann, “Minimizing the condition number of a positive definite matrix by completion”, Numerische Mathematik, vol. 69, 1994, pp. 17-23.

Elsner, L., He, C., Mehrmann, V.: Minimizing the condition number of a positive definite matrix by completion. Numerische Mathematik. 69, 17-23 (1994).

Elsner, Ludwig, He, Chunyang, and Mehrmann, Volker. “Minimizing the condition number of a positive definite matrix by completion”. Numerische Mathematik 69.1 (1994): 17-23.

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