When can forward stable algorithms be composed stably?-Reference-Cited by-同舟云学术

When can forward stable algorithms be composed stably?

Published:2023-05-29 Issue: Volume: Page:
ISSN:0272-4979
Container-title:IMA Journal of Numerical Analysis
language:en
Short-container-title:

Author:

Beltrán Carlos¹,Noferini Vanni²,Vannieuwenhoven Nick³

Affiliation:

1. Department MATESCO, Universidad de Cantabria , Avda. Los Castros s/n, 39005 Santander, Spain

2. Department of Mathematics and Systems Analysis, Aalto University , P.O. Box 11100, FI-00076 Aalto, Finland

3. Department of Computer Science, KU Leuven, Celestijnenlaan 200A , B-3001 Leuven, Belgium

Abstract

Abstract We state some widely satisfied hypotheses, depending only on two functions $g$ and $h$, under which the composition of a forward stable algorithm for $g$ and a forward stable algorithm for $h$ is a forward stable algorithm for the composition $g \circ h$. We show that the failure of these conditions can potentially lead to unstable algorithms. Finally, we list a number of examples to illustrate the new concepts and the usability of the results.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Link

https://academic.oup.com/imajna/advance-article-pdf/doi/10.1093/imanum/drad026/50479917/drad026.pdf

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