An efficient method for the computation of the Feigenbaum constants to high precision

TL;DR

This paper introduces a new efficient algorithm for calculating the Feigenbaum constants with high precision, significantly reducing computational resources and enabling determination to 10,000 decimal places.

Contribution

The paper presents a novel, practical algorithm leveraging linear algebra techniques that improves efficiency and parallelizability for computing Feigenbaum constants.

Findings

Achieved computation of constants to 10,000 decimal places

Reduced time and space complexity compared to previous methods

Algorithm is easily parallelizable

Abstract

We propose a new practical algorithm for computing the Feigenbaum constants {\alpha} and {\delta}, having significantly lower time and space complexity than previously used methods. The algorithm builds upon well-known linear algebra techniques, and is easily parallelizable. An implementation of it has been developed and used to determine both constants to 10,000 decimal places.