Geometric Interpretation of Errors in Multi-Parametrical Fitting Methods Based on Non-Euclidean Norms

The paper completes the multi-parametrical fitting methods, which are based on metrics induced by the non-Euclidean L_q-norms, by deriving the errors of the optimal parameter values. This was achieved using the geometric representation of the residuals sum expanded near its minimum, and the geometric interpretation of the errors. Typical fitting methods are mostly developed based on Euclidean norms, leading to the traditional least–square method. On the other hand, the theory of general fitting methods based on non-Euclidean norms is still under development; the normal equations provide implicitly the optimal values of the fitting parameters, while this paper completes the puzzle by improving understanding the derivations and geometric meaning of the optimal errors.