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 Geometric distance fitting of parabolas in R^3 Commun. Korean Math. Soc.Published online April 12, 2022 Ik Sung Kim Korea Maritime and Ocean University Abstract : We are interested in the problem of fitting a parabola to a set of data points in space. 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~$\mathbb{R}^3$. Our algorithm is mainly based on the steepest descent technique which determines an adequate number $\lambda$ such that $h ( \lambda ) = Q ( u - \lambda \nabla Q\bigl( u \bigr) ) < Q ( u)$. Some numerical examples are given to test our algorithm. Keywords : fitting of parabolas, geometric distance, steepest descent MSC numbers : 65D18 Full-Text :

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