An iterative algorithm for approximating roots of integers

TL;DR

This paper presents an iterative algorithm designed to approximate roots of integers, analyzing its convergence and comparing its performance with existing methods for square roots and rational powers.

Contribution

It introduces a new iterative algorithm for root approximation, providing analysis of convergence rates and comparative performance evaluations.

Findings

The algorithm converges efficiently for various inputs.

It outperforms some established methods in specific cases.

Convergence rates depend on parameter choices.

Abstract

We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating square roots and other rational powers.