When can forward stable algorithms be composed stably?

TL;DR

This paper identifies conditions under which the composition of two stable algorithms remains stable, based on properties of the functions involved, ensuring reliable algorithmic composition.

Contribution

It introduces specific hypotheses involving functions g and h that guarantee the stability of composed algorithms, advancing understanding of algorithm stability in composition.

Findings

Established sufficient conditions for stable composition of algorithms

Demonstrated that certain hypotheses depend only on functions g and h

Provided a framework for analyzing stability in algorithmic composition

Abstract

We state some widely satisfied hypotheses, depending only on two functions $g$ and $h$, under which the composition of a stable algorithm for $g$ and a stable algorithm for $h$ is a stable algorithm for the composition $g \circ h$.