Commun. Korean Math. Soc. Published online January 4, 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