A general lower bound for the asymptotic convergence factor

TL;DR

This paper introduces a broad and easy-to-calculate lower bound for the asymptotic convergence factor applicable to compact subsets of complex numbers with connected complements and finitely many components.

Contribution

It presents a novel, general lower bound for the asymptotic convergence factor that simplifies analysis for specific classes of complex sets.

Findings

Provides a simple, computable lower bound for convergence factors.

Applicable to sets with connected complements and finitely many components.

Enhances understanding of convergence behavior in complex analysis.

Abstract

We provide a rather general and very simple to compute lower bound for the asymptotic convergence factor of compact subsets of the set of complex numbers with connected complement and finitely many connected components .