DERIVATION OF MULTIDIMENSIONAL ELLIPSOIDAL CONVEX MODEL FOR EXPERIMENTAL-DATA

This paper deals with determination of the best ellipsoidal model fitt ing the available limited experimental data. The problem is defined as that of finding the minimum volume ellipsoid containing all experimen tal data. A general transformation matrix for the rotation of N-dimens ional coordinate system is first obtained by the Gramm-Schmidt orthogo nalization procedure. The use of this matrix makes it possible to sear ch in all possible directions to find an ellipsoid with a minimum volu me. The general procedure is illustrated by examples in which the real data is utilized. An invariance property of the response with uncerta in parameters of different physical nature is also discussed.