• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.669-684
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• 1999

We are interested in the problem of fitting a curve to a set of points in the plane in such a way that the sum of the squares of the orthogonal distances to given data points ins minimized. In[1] the prob-lem of fitting circles and ellipses was considered and numerically solved with general purpose methods. Especially in [2] H. Spath proposed a special purpose algorithm (Spath's ODF) for parabolas y-b=$c($\chi$-a)^2$ and for rotated ones. In this paper we present another parabola fitting algorithm which is slightly different from Spath's ODF. Our algorithm is mainly based on the steepest descent provedure with the view of en-suring the convergence of the corresponding quadratic function Q(u) to a local minimum. Numerical examples are given.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.915-938
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• 2022

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.