Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GEOMETRIC DISTANCE FITTING OF PARABOLAS IN ℝ3

  • Kim, Ik Sung (Department of Data Information Korea Maritime and Ocean University)
  • Received : 2021.07.30
  • Accepted : 2021.10.07
  • Published : 2022.07.31
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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.

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References

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