Complete algebraic classification of the hypersurfaces of the maximum inaccuracies of an indirectly measurable variable

TL;DR

This paper provides a complete algebraic classification of hypersurfaces representing maximum inaccuracies of an indirectly measurable variable in second degree approximation, enhancing the understanding of measurement precision.

Contribution

It introduces a full algebraic classification of the quadratic hypersurfaces of maximum inaccuracies, advancing the theoretical framework for measurement accuracy evaluation.

Findings

Maximum inaccuracies are quadrics of the inaccuracies of the variables.

These quadrics describe specific types of parabolic hypersurfaces.

A dimensionless scale for quality evaluation is defined based on these inaccuracies.

Abstract

Let an indirectly measurable variable be represented as a function of a finite number of directly measurable variables . In our previous researches we: 1) represented the maximum inaccuracies of in first degree of approximation as linear functions of the inaccuracies of ; 2) defined the spaces of the maximum inaccuracies and we defined a dimensionless scale for quality (accuracy) evaluation of an experiment in them; 3) introduced the maximum inaccuracies in second degree of approximation. In the current paper we prove that the maximum inaccuracies of in second degree of approximation are quadrics of the inaccuracies of and that these forms describe certain types of quadric hypersurfaces of parabolic class. Moreover: 1) we give a complete algebraic classification of these hypersurfaces; 2) we define a dimensionless scale for quality (accuracy) evaluation of the experiment given the maximum inaccuracies in second degree of approximation.