An Extended Newton-Type Method In R And Polynomiography Via Different Iterative Methods

TL;DR

This paper introduces a new Newton-type iterative method for solving scalar nonlinear equations, demonstrating convergence under weaker conditions and producing visually appealing graphics.

Contribution

The paper presents a novel Newton-type method with convergence proven under weaker assumptions, enhancing solution visualization in polynomiography.

Findings

Convergence under weaker conditions than traditional methods

Generation of aesthetically pleasing polynomiography images

Validation of the method through fixed point techniques

Abstract

The aim of this paper is to introduce a new Newton-type iterative method and then to show that this process converges to the unique solution of the scalar nonlinear equation f(x)=0 under weaker conditions involving only f and f' by fixed point techniques. Also, by using this iteration process quite new nicely looking graphics are obtained.