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has been cited by the following article:

• TITLE: An Automated Model for Fitting a Hemi-Ellipsoid and Calculating Eigenvalues Using Matrices

  AUTHORS: Alicia R. Billington, Peter J. Fabri, William E. Lee III

  KEYWORDS: Modeling; Response Surfaces; Ellipsoid

  JOURNAL NAME: Applied Mathematics, Vol.5 No.2, January 17, 2014

  ABSTRACT: Ellipsoid modeling is essential in a variety of fields, ranging from astronomy to medicine. Many response surfaces can be approximated by a hemi-ellipsoid, allowing estimation of shape, magnitude, and orientation via orthogonal vectors. If the shape of the ellipsoid under investigation changes over time, serial estimates of the orthogonal vectors allow time-sequence mapping of these complex response surfaces. We have developed a quantitative, analytic method that evaluates the dynamic changes of a hemi-ellipsoid over time that takes data points from a surface and transforms the data using a kernel function to matrix form. A least square analysis minimizes the difference between actual and calculated values and constructs the corresponding eigenvectors. With this method, it is possible to quantify the shape of a dynamic hemi-ellipsoid over time. Potential applications include modeling pressure surfaces in a variety of applications including medical.