  Multi-dimensional distributions of discrete data that resemble ellipsoids
arise in numerous areas of science, statistics, and computational geometry. We
describe a complete algebraic algorithm to determine the quadratic form
specifying the equation of ellipsoid for the boundary of such multi-dimensional
discrete distribution. In this approach, the equation of ellipsoid is
reconstructed using a set of matrix equations from low-dimensional projections
of the input data. We provide a Mathematica program realizing the full
implementation of the ellipsoid reconstruction algorithm in an arbitrary number
of dimensions. To demonstrate its many potential uses, the fast reconstruction
method is applied to quasi-Gaussian statistical distributions arising in
elementary particle production at the Large Hadron Collider.
