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논문KCI 등재

Total Least Squares Fitting with Quadrics

Helmuth Spath
한국수학교육학회|2004.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제11권 제2호|pp. 105-115

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참고문헌

주제분류수학

초록

Abstract

A computational algorithm is developed for ¯tting given data in the plane or in 3-space by implicitly de¯ned quadrics. Implicity implies that the type of the quadric is part of the model and need not be known in advance. Starting with some estimate for the coe±cients of the quadric the method will alternatively determine the shortest distances from the given points onto the quadric and adapt the coe±cients such as to reduce the sum of those squared distances. Numerical examples are given.

참고문헌 (15)

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  8. Boston, "Mathematical algorithms for linear regression Translated and revised fromthe 1987 German original by the author" (1992), Academic Press Inc
  9. "Least-squares ？tting by circles", 57(2), pp.179~185 (1996)
  10. "Orthogonal squared distance ¯tting with parabolas" (1996)
  11. "Least-squares ？tting of ellipses and hyperbolas", 12(3), pp.329~341 (1997)
  12. "Orthogonal least squares ？tting by conic sections. Recent advances in totalleast squares techniques and errors-in-variables modeling"
  13. "Least-square ？tting with spheres", 96(1), pp.191~199 (1998)
  14. "Estimating the parameters of an ellipse when angular di？？erences are known", 14, pp.491~500 (1999)
  15. D. A. Turner,, "An algorithm for ？ tting anellipsoid to data to be found in www" (1999)

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