Novel Computer Software for Interpolation and Approximation of Ravine and Stiff Digital Dependencies Using Root-Polynomoal and Root-Fractional-Rational Functions

Abstract

The article considers the possibilities of solving interpolation and approximation problems using special types of functions, such as root polynomials and root fractional rational, and provides relevant examples. It is prove, that the use of root polynomial functions is especially effective for interpolation and approximation of numerical dependencies with a ravine data set, and the use of root fractional rational functions gives the best results for various data sets with a more rigid functional dependence. To solve the approximation problem, a new approximation by reference points is proposed and tested. With a small number of points in the data set for the approximation problem, equal to twenty or less, the convergence of the proposed method is usually guaranteed. In general, the proposed algorithms are very universal and can be easily adapted to any complex problems. All the proposed methods are implemented and tested in the newly developed computer software created in the Python programming language.