An Investigation on using Lagrange, Newton and Least Square Methods for Generating Nonlinear Interpolation Function for the Measuring Instruments

Abstract

This research is considered the milestone for metrologists to choose the appropriate method for determination of the nonlinear interpolation function for the measuring instruments. Three methods of generating the interpolation polynomial equations were investigated; Newton, Lagrange, and Least Square method. The response of the measuring instruments under investigation was calculated and compared with the experimental results. Least Square method was found that it is the most accurate and most realistic approach to determine the interpolation polynomial function for the measuring instruments. It is recommended to use Least Square method rather than other methods to interpolating the polynomial equation. This recommendation is very important for metrologist as well as for measuring instruments applicant. This article is millstone to determine the response of the measuring instrument at non calibrated points in the calibrated range.

Calibration approach to quantify nonlinearity of MEMS pore pressure sensors using optimal interpolation

“…Thus, the sensor input-output's relationship can be solved using interpolation or least square approximation to define polynomial function for such a set of data in order to reach an efficient and accurate outcome (e.g. [23,[30][31][32][33][34][35]). Lagrange interpolation (LI) method is a proper choice for low-cost calibration scheme where the order of polynomial is higher degree.…”