Orthonormal Polynomial Approximation of Mineral Water Data with Errors in Both Variables

TL;DR

This paper presents an orthonormal polynomial expansion method to model mineral water data with errors in both variables, providing accurate approximations and derivatives while accounting for measurement uncertainties.

Contribution

It introduces a novel application of orthonormal polynomial expansion to data with errors in both variables, including a weighting approach and new evaluation criteria.

Findings

Effective approximation of mineral water data with errors in both variables.

Numerical results demonstrate the accuracy of the orthonormal polynomial method.

The method provides reliable derivatives and error estimates for the data.

Abstract

In this paper we introduce the data from mineral water probe with errors in both variables. For this case we apply our orthonormal polynomial expansion(OPEM) method to describe the data in the new error corridor. It receives the approximating curves and their derivatives including the errors by weighting approach. The numerical method and approximation results are presented and discussed. The special criteria are carried out for orthonormal and evaluated from it usual expansion. The numerical results are shown in tables and figures.