MINIMIZATION OF THE NORM, THE NORM OF THE INVERSE AND THE CONDITION NUMBER OF A MATRIX BY COMPLETION

We study the problem of minimizing the norm, the norm of the inverse a nd the condition number with respect to the spectral norm, when a subm atrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Wein berger. This new approach can then also be used to characterize the co mpletions that minimize the norm of the inverse. For the problem of op timizing the condition number we give a partial result.