The our aim of this work is to present some theoretical aspects and numerical results about the algebraic ellipse fitting to 2D data, showing the advantages and also the drawbacks of this procedure. All the necessary theoretical aspects are rigorously presented, as well as many examples that justify the usefulness of the method of algebraic fitting. Consulting the graphical obtained results, one may notice that the accuracy corresponds for the practical use of this method. Consulting the literature, we observe that the main part of scientific works deal with the geometric fitting and the algebraic fitting is considered only to show its deficiencies with respect to the geometric fitting. Our hope is that the algebraic fitting will be reconsidered and used in the cases when it is applicable.

Key words: ellipse, algebraic fitting, least-squares method, parametric equations, accuracy

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