Web application for automated selection and display of optimal interpolants for one-dimensional dependencies

Abstract

The experimental results presented in the form of tables sometimes do not allow to clearly characterize the physical essence of the studied processes, to establish the nature of the functional dependence. The presentation of the obtained results in the form of graphical dependencies, which make it possible to display the relationships between the parameters under study in a concise and understandable form, is one of the methods of processing experimental data. Then there is a need to display such results in the form of mathematical dependencies. Therefore, the search for the optimal interpolant is a relevant scientific and practical task. A methodology is proposed and software for a web application for automated selection and display of optimal interpolants for one-dimensional dependencies given in tabular form is developed. The developed web application represents a website written in Java using Hibernate, JSF frameworks and PrimeFaces library, which can be used to represent in mathematical form the dependencies of the researched processes and phenomena in many areas of activity. In order to obtain interpolants, the interpolation method was applied. Complete polynomials of the first, second, and third degrees and some of the most typical one-dimensional mathematical dependencies were used as interpolants. To assess the quality of interpolation, the coefficient of determination [11] was used. The optimal one is considered to be the one from the obtained interpolants for which the value of the coefficient of determination is the largest. One-dimensional graphs of optimal interpolants and their analytical expressions for some dependencies obtained experimentally are presented