Minimizing the condition number of a positive definite matrix by completion

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

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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.
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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.
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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