# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1706.08400