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Perturbation analysis for circles, spheres, and generalized hyperspheres fitted to data by geometric total least-squares
Author(s):
Yves
Nievergelt.
Journal:
Math. Comp.
73
(2004),
169-180.
MSC (2000):
Primary 65D10, 51M16
Posted:
August 19, 2003
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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.
References:
-
- 1.
- Åke Björck, Numerical methods for least squares problems, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1996. MR 97g:65004
- 2.
- T. Altherr and J. Seixas, Cherenkov ring recognition using a nonadaptable network, Nuclear Instruments & Methods in Physics Research, Section A A317 (1992), no. 1, 2, 335-338.
- 3.
- Fred L. Bookstein, Fitting conic sections to scattered data, Computer Graphics and Image Processing 9 (1979), 56-71.
- 4.
- I. D. Coope, Circle fitting by linear and nonlinear least squares, Journal of Optimization Theory and Applications 76 (1993), no. 2, 381-388. MR 93k:65054
- 5.
- J. F. Crawford, A noniterative method for fitting circular arcs to measured points, Nuclear Instruments and Methods 211 (1983), no. 2, 223-225.
- 6.
- I. Duerdoth, Track fitting and resolution with digital detectors, Nuclear Instruments and Methods 203 (1982), no. 1-3, 291-297.
- 7.
- Wendell Helms Fleming, Functions of several variables, second ed., Springer-Verlag, New York, NY, 1987, Corrected third printing.
- 8.
- Walter Gander, Gene H. Golub, and Rolf Strebel, Least-squares fitting of circles and ellipses, BIT 34 (1994), 558-578. MR 97j:65020
- 9.
- M. Hansroul, H. Jeremie, and D. Savard, Fast circle fit with the conformal mapping method, Nuclear Instruments & Methods in Physics Research, Section A A270 (1988), no. 2, 3, 498-501.
- 10.
- Peter Henrici, Essentials of numerical analysis with pocket calculator demonstrations, Wiley, New York, NY, 1982. MR 83h:65002
- 11.
- -, Solutions manual essentials of numerical analysis with pocket calculator demonstrations, Wiley, New York, NY, 1982.
- 12.
- Nicholas J. Higham, Accuracy and stability of numerical algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1996. MR 97a:65047
- 13.
- V. Karimäki, Effective circle fitting for particle trajectories, Nuclear Instruments & Methods in Physics Research, Section A A305 (1991), no. 1, 187-191.
- 14.
- I. Kasa, A circle fitting procedure and its error analysis, IEEE Transactions on Instrumentation and Measurement 25 (1976), no. 1, 8-14.
- 15.
- Charles L. Lawson and Richard J. Hanson, Solving least squares problems, Classics In Applied Mathematics, vol. 15, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1995. MR 96d:65067
- 16.
- L. Moura and R. Kitney, A direct method for least-squares circle fitting, Computer Physics Communications 64 (1992), no. 1, 57-63. MR 92a:65052
- 17.
- Yves Nievergelt, A tutorial history of least squares with applications to astronomy and geodesy, Numerical Anslysis: Historical Develoments in the 20th Century (Amsterdam) (Claude Brezinski and Luc Wuytack, eds.), Elsevier, 2001, pp. 77-112. MR 2001e:65002
- 18.
- Vaughan Pratt, Direct least-squares fitting of algebraic surfaces, ACM Computer Graphics 21 (1987), no. 4, 145-152. MR 90e:65019
- 19.
- Chris Rorres and David Gilman Romano, Finding the center of a circular starting line in an ancient Greek stadium, SIAM Review 39 (1997), no. 4, 745-754. MR 98i:01002
- 20.
- Helmut Späth, Least-squares fitting with spheres, Journal of Optimization Theory and Applications 96 (1998), no. 1, 191-199. MR 98m:65065
- 21.
- G. W. Stewart, On the early history of the singular value decomposition, SIAM Review 35 (1993), no. 4, 551-566. MR 94f:15001
- 22.
- Sabine Van Huffel and Joos Vandewalle, The total least squares problem: Computational aspects and analysis, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1991. MR 93b:65001
- 23.
- Per-Åke Wedin, Perturbation bounds in connection with singular value decomposition, BIT 12 (1972), no. 1, 99-111. MR 46:9071
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Additional Information:
Yves
Nievergelt
Affiliation:
Department of Mathematics, Eastern Washington University, 216 Kingston Hall, Cheney, Washington 99004-2418
Email:
ynievergelt@ewu.edu
DOI:
10.1090/S0025-5718-03-01613-2
PII:
S 0025-5718(03)01613-2
Keywords:
Fitting,
geometric,
circles,
spheres,
total least-squares
Received by editor(s):
January 3, 2001
Received by editor(s) in revised form:
April 24, 2002
Posted:
August 19, 2003
Additional Notes:
Work done at the University of Washington during a leave from Eastern Washington University.
Copyright of article:
Copyright
2003,
American Mathematical Society
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