Automation of Initial Approximations Choice for Solving Nonlinear Equations by Numerical Methods

Abstract

The choice of initial approximations for finding the roots of nonlinear equations affects the convergence of methods. This paper presents the algorithm for finding initial approxi mations for computing the roots of nonlinear equations for various numerical methods. This algorithm is used for compiling educational tasks. The implementation is written in the Python programming language. The article provides pseudocode for the algorithm. The possibilities of the specified algorithm and auxiliary functions are considered, and the process of the program operation is described in detail. The results of a comparative analysis of the number of iterations required to find roots using the initial approximati on search algorithm and the manual method of selecting root localization intervals are presented. The proposed approach has demonstrated its efficiency on 520 different nonli near equations.