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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Perturbation analysis for circles, spheres, and generalized hyperspheres fitted to data by geometric total least-squares
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by Yves Nievergelt;
Math. Comp. 73 (2004), 169-180
DOI: https://doi.org/10.1090/S0025-5718-03-01613-2
Published electronically: August 19, 2003

Abstract:

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.
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Bibliographic Information
  • Yves Nievergelt
  • Affiliation: Department of Mathematics, Eastern Washington University, 216 Kingston Hall, Cheney, Washington 99004-2418
  • Email: ynievergelt@ewu.edu
  • Received by editor(s): January 3, 2001
  • Received by editor(s) in revised form: April 24, 2002
  • Published electronically: August 19, 2003
  • Additional Notes: Work done at the University of Washington during a leave from Eastern Washington University.
  • © Copyright 2003 American Mathematical Society
  • Journal: Math. Comp. 73 (2004), 169-180
  • MSC (2000): Primary 65D10, 51M16
  • DOI: https://doi.org/10.1090/S0025-5718-03-01613-2
  • MathSciNet review: 2034115