GEOMETRIC DISTANCE FITTING OF PARABOLAS IN ℝ³

We are interested in the problem of fitting a parabola to a set of data points in &#x211D;³. 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 &#x211D;³. Our algorithm is mainly based on the steepest descent technique which determines an adequate number &#x03BB; such that h(&#x03BB;) = Q(u - &#x03BB;&#x1D6C1;Q(u)) < Q(u). Some numerical examples are given to test our algorithm.