Orlicz–Legendre Ellipsoids

Löwner-john Ellipsoids

Before giving the mathematical description of the Löwner-John ellipsoids and pointing out some of their far-ranging applications, I briefly illuminate the adventurous life of the two eminent mathematicians, by whom the ellipsoids are named: Charles Loewner (Karel Löwner) and Fritz John. Karel Löwner was born into a Jewish family in Lány, a small town about 30 km west of Prague, in 1893. Due to ...

Packing Ellipsoids with Overlap

The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. Convergence results are proved and computationa...

Intersection of Ellipsoids

Minimum Volume Enclosing Ellipsoids

Two different methods for computing the covering ellipses of a set of points are presented. The first method finds the optimal ellipsoids with the minimum volume. The second method uses the first and second moments of the data points to compute the parameters of an ellipsoid that covers most of the points. A MATLAB software is written to verify the results.

Surface Area of Ellipsoids

A. We study the surface area of an ellipsoid in E as the function of the lengths of theirmajor semi-axes. Wewrite down an explicit formula as an integral over Sn−1, use the formula to derive convexity properties of the surface area, to sharpen the estimates given [6], to produce asymptotic formulas in large dimensions, and to give an expression for the surface in terms of the Lauricella ...