Control of Dynamics of the Modified Newton-Raphson Algorithm

Abstract

Many algorithms that iteratively find solution of an equation are described in the literature. In this article we propose an algorithm that is based on the Newton-Raphson root finding method and which uses an adaptation mechanics. The adaptation mechanics is based on a linear combination of some membership functions and allows a better control of algorithm's dynamics. The proposed approach allows to visualize the adaptation mechanics impact on the operation of the algorithm. Moreover, various iteration processes and their operation mechanics are discussed in this research. The understanding of the impact of the proposed modifications on the algorithm's operation can be helpful at using other algorithms. The obtained visualizations have also an artistic potential and can be used for instance in creating mosaics, wallpapers etc.