ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):65F35, 15A12
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. We consider the problem of minimizing the spectral condition number of a positive definite matrix by completion: $$\min\left\{ {\rm cond}\left(\mat{cc} A & B^{\rm H} \\ B & X \rix\right): \mat{cc} A & B^{\rm H} \\ B & X \rix \mbox {\rm positive definite} \right\},$$ \noindent where $A$ is an $n\times n$ Hermitian positive definite matrix, $B$ a $p\times n$ matrix and $X$ is a free $p\times p$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050077
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