Ellipsoidal Bounds for the Vector Sum of Two Ellipsoids

摘要

Given two sets of vectors E sub 1 and E sub 2 consisting of all vectors inside and on the boundary of two given ellipsoids, the vector sum of these two sets is defined as the set of all vectors that can be obtained by adding arbitrary vectors of each set. Ellipsoids bounding the vector sum are found by constructing an inhomogeneous initial value problem for a system of ordinary differential equation such that a well defined set of solutions for a certain value of the independent variable gives exactly the vectors of this vector sum. This set is then bounded by a suitable differential inequality. The result is verified by direct computation. The relations between the bounding ellipsoid and the vector sum are studied in detail. (Author)