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http://dx.doi.org/10.4134/CKMS.c210258

GEOMETRIC DISTANCE FITTING OF PARABOLAS IN ℝ3  

Kim, Ik Sung (Department of Data Information Korea Maritime and Ocean University)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 915-938 More about this Journal
Abstract
We are interested in the problem of fitting a parabola to a set of data points in ℝ3. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in ℝ3. Our algorithm is mainly based on the steepest descent technique which determines an adequate number λ such that h(λ) = Q(u - λ𝛁Q(u)) < Q(u). Some numerical examples are given to test our algorithm.
Keywords
Fitting of parabolas; geometric distance; steepest descent;
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Times Cited By KSCI : 1  (Citation Analysis)
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