Abstract
This paper discusses the computational problem of fitting data by an implicitly defined function depending on several parameters. The emphasis is on the technique of algebraic fitting off(x, y; p) = 0 which can be treated as a linear problem when the parameters appear linearly. Various constraints completing the problem are examined for their effectiveness and in particular for two applications: fitting ellipses and functions defined by the Lotka-Volterra model equations. Finally, we discuss geometric fitting as an alternative, and give examples comparing results.
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Varah, J.M. Least squares data fitting with implicit functions. Bit Numer Math 36, 842–854 (1996). https://doi.org/10.1007/BF01733795
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DOI: https://doi.org/10.1007/BF01733795