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Perturbation Analysis for Circles, Spheres, and Generalized Hyperspheres Fitted to Data by Geometric Total Least-Squares
Mathematics of Computation
Vol. 73, No. 245 (Jan., 2004), pp. 169-180
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/4099863
Page Count: 12
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A continuous extension of the objective function to a projective space guarantees that for each data set there exists at least one hyperplane or hypersphere minimizing the average squared distance to the data. For data sufficiently close to a hypersphere, as the collinearity of the data increases, so does the sensitivity of the fitted hypersphere to perturbations of the data.
Mathematics of Computation © 2004 American Mathematical Society