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

1 March 1995

journal article
research article
Published by Wiley in Numerical Linear Algebra with Applications

Vol. 2 (2) , 155-171
https://doi.org/10.1002/nla.1680020207

Abstract

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.

Keywords

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