Robustness for the Starting Point of Two Iterative Methods for Fitting Debye or Cole–Cole Models to a Dielectric Permittivity Spectrum

Abstract

Curve-fitting means the determination of the set of parameters that best fit the input data set as expressed by a given function that is usually non-linear. The paper addresses the curve fitting of Debye and Cole–Cole models to a dielectric permittivity spectrum. The success of a nonlinear curve fit heavily depends on the choice of the algorithm and how close the starting point is to the solution. For these reasons, two different algorithms, the Levenberg–Marquardt and the Variable Projection algorithms, were used for constrained optimization and compared, with particular reference to robustness with respect to the choice of the starting point of the reconstruction procedure. The dielectric spectrum of blood plasma with different glucose concentrations is taken as reference data and a Monte Carlo analysis was conducted to evaluate accuracy and precision in the two methods provided as the distance of the initial parameters from the true value’s changes. In general, both algorithms with constraints on the parameters provide good results for practical situations, although the Variable Projection Algorithm has a greater computational burden for large data sets.