000168390 001__ 168390 000168390 005__ 20260204153543.0 000168390 0247_ $$2doi$$a10.1002/cpe.70305 000168390 0248_ $$2sideral$$a147865 000168390 037__ $$aART-2025-147865 000168390 041__ $$aeng 000168390 100__ $$aKjelgaard Mikkelsen, Carl Christian 000168390 245__ $$aHow Accurate is Richardson's Error Estimate? 000168390 260__ $$c2025 000168390 5060_ $$aAccess copy available to the general public$$fUnrestricted 000168390 5203_ $$aABSTRACT 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. 000168390 536__ $$9info:eu-repo/grantAgreement/ES/AEI/PID2022-136454NB-C22$$9info:eu-repo/grantAgreement/ES/DGA/T58-23R 000168390 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc$$uhttps://creativecommons.org/licenses/by-nc/4.0/deed.es 000168390 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000168390 700__ $$0(orcid)0000-0002-1891-4359$$aLópez-Villellas, Lorién$$uUniversidad de Zaragoza 000168390 7102_ $$15007$$2035$$aUniversidad de Zaragoza$$bDpto. Informát.Ingenie.Sistms.$$cÁrea Arquit.Tecnología Comput. 000168390 773__ $$g37, 27-28 (2025), e70305 [23 pp.]$$pConcurr. Comput.-Pract. Exp.$$tCONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE$$x1532-0626 000168390 8564_ $$s1020541$$uhttps://zaguan.unizar.es/record/168390/files/texto_completo.pdf$$yVersión publicada 000168390 8564_ $$s2300110$$uhttps://zaguan.unizar.es/record/168390/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000168390 909CO $$ooai:zaguan.unizar.es:168390$$particulos$$pdriver 000168390 951__ $$a2026-02-04-13:15:04 000168390 980__ $$aARTICLE