Let ${\cal S}$ denote the convex hull of $m$ full-dimensional ellipsoids in $\mathbb{R}^n$. Given $\epsilon > 0$ and $\delta > 0$, we study the problems of computing a $(1+ \epsilon)$-approximation to the minimum volume covering ellipsoid of ${\cal S}$ and a $(1 + \delta)n$-rounding of ${\cal S}$. We extend the first-order algorithm of Kumar and [J...

On the Minimum Volume Covering Ellipsoid of Ellipsoids

10.1137/050622560