Hyperspheres and hyperplanes fitted seamlessly by algebraic constrained total least-squares

Linear Algebra and Its Applications

Volumn 331, Issue 1-3, 2001, Pages 43-59

  Nievergelt, Yves ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Algebraic; Circles; Fitting; Hyperspheres; Spheres; Total least squares

Indexed keywords

EID: 0035400327     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00263-4     Document Type: Article

References (26)

1. Åke Björk, Numerical Methods for Least Squares Problems, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1996.
2. Bookstein F.L. Fitting conic sections to scattered data. Comput. Graphics Image Process. 9:1979;56-71.
3. Coope I.D. Circle fitting by linear and nonlinear least squares. J. Optim. Theory Appl. 76(2):1993;381-388.
4. Cox M.G., Jones H.M. An algorithm for least-squares circle fitting to data with specified uncertainty ellipses. IMA J. Numer. Anal. 9(3):1989;285-298.
5. Crawford J.F. A non-iterative method for fitting circular arcs to measured points. Nucl. Instr. and Meth. 211(2):1983;223-225.
6. Edwards Deming W. Statistical Adjustment of Data. 1964;Dover, New York.
7. Gander W., Golub G.H., Strebel R. Least-squares fitting of circles and ellipses. BIT. 34:1994;558-578.
8. Golub G.H., Hoffman A., Stewart G.W. A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Linear Algebra Appl. 88&89:1987;317-327.
9. Golub G.H., Van Loan C.F. An analysis of the total least squares problem. SIAM J. Numer. Anal. 17(6):1980;883-893.
10. Henrici P. Essentials of Numerical Analysis with Pocket Calculator Demonstrations. 1982;Wiley, New York.
11. H. Karttunen, P. Kröger, H. Oja, M. Poutanen, K. Johan Donner (Eds.), Fundamental Astronomy, second enlarged ed., Springer, New York, 1994.
12. Kȧsa I. A circle fitting procedure and its error analysis. IEEE Trans. Instrum. Meas. 25(1):1976;8-14.
13. C.L. Lawson, R.J. Hanson, Solving Least Squares Problems, Classics in Applied Mathematics, vol. 15, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1995.
14. Mamakov A.S. System of selenodetic coordinates based on heliometric observations of the Moon at kazan. The Moon and the Planets. 21(1):1979;19-23.
15. Mirsky L. Symmetric gauge functions and unitarily invariant norms. Quart. J. Math. (Oxford). 11:1960;50-59.
16. Moura L., Kitney R. A direct method for least-squares circle fitting. Comput. Phys. Commun. 64(1):1992;57-63.
17. Nievergelt Y. Computing circles and spheres of arithmetic least squares. Comput. Phys. Commun. 81(3):1994;343-350.
18. Nievergelt Y. Total least squares: state-of-the-art regression in numerical analysis. SIAM Rev. 36(2):1994;258-264.
19. Pratt V. Direct least-squares fitting of algebraic surfaces. ACM Comput. Graphics. 21(4):1987;145-152.
20. Rorres C., Romano D.G. Finding the center of a circular starting line in an ancient Greek stadium. SIAM Rev. 39(4):1997;745-754.
21. Schmidt E. Zur Theorie der linearen und nichtlinearen Integralgleichungen, 1. Teil: Entwicklung willkürlicher Funktionen nach Systemen vorgeschriebener. Math. Ann. 63:1907;433-476.
22. Späht H. Least-squares fitting with spheres. J. Optim. Theory Appl. 96(1):1998;191-199.
23. Späth H. Orthogonal distance fitting by circles and ellipses with given area. Comput. Statist. 12:1997;343-354.
24. Stewart G.W. On the early history of the singular value decomposition. SIAM Rev. 35(4):1993;551-566.
25. S.V. Huffel, J. Vandewalle, The Total Least Squares Problem: Computational Aspects and Analysis, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1991.
26. Wedin P.-Å. Perturbation bounds in connection with singular value decomposition. BIT. 12(1):1972;99-111.