Abstract
Let a family of curves or surfaces be given in implicit form via the model equationf (x,Β)=0, wherex ε ℝd andΒ ε ℝm is a parameter vector. We present a trust region algorithm for solving the problem:find a parameter vector Β * such that the contour f(x,Β *)=0is a best fit to given data {zi} ni =1 ⊂ ℝd in a least squares sense. Specifically, we seekΒ * and {x * i } n i =1 such thatf (x *i ,Β *) = 0,i=1,...,n, and ∑ n i=1 ‖z i −x * i ‖ 22 is minimal. The termorthogonal distance regression is used to describe such constrained nonlinear least squares problems.
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Helfrich, H.P., Zwick, D. A trust region method for implicit orthogonal distance regression. Numer Algor 5, 535–545 (1993). https://doi.org/10.1007/BF02108668
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DOI: https://doi.org/10.1007/BF02108668