SMU Journal of Undergraduate Research


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 an 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 direct reconstruction method is applied to quasi-Gaussian statistical distributions arising in elementary particle production at the Large Hadron Collider.

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License