Convergence Acceleration Techniques

TL;DR

This paper reviews numerical methods designed to accelerate convergence and sum divergent series, significantly reducing computational time across various scientific fields such as bioinformatics, physics, and mathematics.

Contribution

It introduces and discusses techniques for speeding up convergence and summation of divergent series, applicable in multiple scientific disciplines.

Findings

Methods can reduce computing time by orders of magnitude.

Applicable to a wide range of fields including biology, physics, and mathematics.

Enhances efficiency of numerical computations involving series.

Abstract

This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the acceleration of slowly convergent and the summation of divergent series that are ubiquitous in relevant applications. The computing time is reduced in many cases by orders of magnitude.