Minimizing the condition number
of a positive definite matrix by completion |
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| Authors: | L Elsner C He V Mehrmann |
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| Institution: | (1) Fakult{\"a}t f{\"u}r Mathematik, Universit{\"a}t Bielefeld, D-33615 Bielefeld, Germany , DE;(2) Fachbereich Mathematik, PSF 964, TU-Chemnitz-Zwickau, D-09009 Chemnitz, Germany , DE |
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| Abstract: | Summary. We consider the problem of minimizing
the spectral condition number of a positive definite matrix
by completion:
\noindent where is
an Hermitian positive definite
matrix, a matrix and is
a free 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.
Received October 15, 1993 |
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| Keywords: | Mathematics Subject Classification (1991):65F35 15A12 |
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