  Dearing and Zeck presented a dual algorithm for the problem of the minimum
covering ball in $\mathbb{R}^n$. Each iteration of their algorithm has a
computational complexity of at least $\mathcal O(n^3)$. In this paper we
propose a modification to their algorithm that, together with an implementation
that uses updates to the QR factorization of a suitable matrix, achieves a
$\mathcal O(n^2)$ iteration.
