A class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances

Given a family of curves or surfaces in R s , an important problem is that of finding a member of the family which gives a “best” fit to m given data points. A criterion which is relevant to many application areas is orthogonal distance regression, where the sum of squares of the orthogonal distance...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2003-09, Vol.158 (2), p.277-296
Main Authors: Atieg, A., Watson, G.A.
Format: Article
Language:English
Subjects:
Approximations and expansions
Exact sciences and technology
Gauss–Newton
Least squares
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Orthogonal distances
Sciences and techniques of general use
Unified framework
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Summary:Given a family of curves or surfaces in R s , an important problem is that of finding a member of the family which gives a “best” fit to m given data points. A criterion which is relevant to many application areas is orthogonal distance regression, where the sum of squares of the orthogonal distances from the data points to the surface is minimized. For certain types of fitting problem, attention has recently focussed on the use of an iteration process which forces orthogonality to hold at every iteration and uses steps of Gauss–Newton type. Within this framework a number of different methods has recently emerged, and the purpose of this paper is to place these methods into a unified framework and to make some comparisons.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(03)00448-5