168390 20260204153543.0 doi 10.1002/cpe.70305 sideral 147865 ART-2025-147865 eng Kjelgaard Mikkelsen, Carl Christian How Accurate is Richardson's Error Estimate? 2025 ABSTRACT We consider the fundamental problem of estimating the difference between the exact value and approximations that depend on a single real parameter . It is well‐known that if the error satisfies an asymptotic expansion, then we can use Richardson extrapolation to approximate . In this paper, our primary concern is the accuracy of Richardson's error estimate , that is, the size of the relative error . In practice, the computed value is different from the exact value . We show how to determine when the computational error is irrelevant and how to estimate the accuracy of Richardson's error estimate in terms of Richardson's fraction . We establish monotone convergence theorems and derive upper and lower bounds for in terms of and . We classify asymptotic error expansions according to their practical value rather than the order of the primary error term. We present a sequence of numerical experiments that illustrate the theory. Weierstrass's function is used to define a sequence of smooth problems for which it is impractical to apply Richardson's techniques. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/AEI/PID2022-136454NB-C22 info:eu-repo/grantAgreement/ES/DGA/T58-23R info:eu-repo/semantics/openAccess by-nc https://creativecommons.org/licenses/by-nc/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion López-Villellas, Lorién Universidad de Zaragoza (orcid)0000-0002-1891-4359 5007 035 Universidad de Zaragoza Dpto. Informát.Ingenie.Sistms. Área Arquit.Tecnología Comput. 37, 27-28 (2025), e70305 [23 pp.] Concurr. Comput.-Pract. Exp. CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE 1532-0626 1020541 http://zaguan.unizar.es/record/168390/files/texto_completo.pdf Versión publicada 2300110 http://zaguan.unizar.es/record/168390/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:168390 articulos driver 2026-02-04-13:15:04 ARTICLE