Computing minimum-volume enclosing ellipsoids

Abstract For a given multidimensional data set (point cloud), we investigate methods for computing the minimum-volume enclosing ellipsoid (MVEE), which provides an efficient representation of that is useful in many applications, including analysis, optimal design, and computational geometry. Contrary to conventional wisdom, demonstrate careful exploitation problem structure can enable high-order (Newton Newton-like) with superlinear convergence rates scale very large MVEE problems. We also introduce hybrid method combines benefits both low-order methods, along new initialization schemes further enhance performance. Observing cost depends significantly on particular distribution data, kurtosis serves as excellent indicator difficulty guidance choosing appropriate solution algorithm initialization.