000169371 001__ 169371 000169371 005__ 20260225105429.0 000169371 0247_ $$2doi$$a10.1007/s10092-026-00683-2 000169371 0248_ $$2sideral$$a148320 000169371 037__ $$aART-2026-148320 000169371 041__ $$aeng 000169371 100__ $$aDíaz, Pablo$$uUniversidad de Zaragoza 000169371 245__ $$aPerturbation theory and error analysis for the Cauchy formula 000169371 260__ $$c2026 000169371 5060_ $$aAccess copy available to the general public$$fUnrestricted 000169371 5203_ $$aIn this work, we analyze the numerical behavior of the classical Cauchy identity & sum;(lambda )s(lambda)(a(1),... , a(n))s(lambda)(x(1), ... , x(m)) = & prod;(n)(j=1) & prod;(m)(i=1) 1/1-a(j)x(i), by developing perturbation and running error analyses. We show that relative perturbations in the nodes x(i) and coefficients a(j) only induce small relative changes in the output provided some relative gaps are sufficiently large. We also propose an algorithm computing a posteriori relative error bound with low computational overhead. Finally, we derive truncation error bounds for the Schur expansion of the formula. Numerical experiments confirm the sharpness of the theoretical results and illustrate the effectiveness of the proposed bounds in practice. 000169371 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00$$9info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T 000169371 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000169371 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000169371 700__ $$0(orcid)0000-0002-6497-7158$$aKhiar, Yasmina$$uUniversidad de Zaragoza 000169371 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, Esmeralda$$uUniversidad de Zaragoza 000169371 700__ $$0(orcid)0000-0003-1550-8168$$aRoyo-Amondarain, Eduardo$$uUniversidad de Zaragoza 000169371 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000169371 773__ $$g63, 1 (2026), [17 pp.]$$pCalcolo$$tCALCOLO$$x0008-0624 000169371 8564_ $$s3434954$$uhttps://zaguan.unizar.es/record/169371/files/texto_completo.pdf$$yVersión publicada 000169371 8564_ $$s959322$$uhttps://zaguan.unizar.es/record/169371/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000169371 909CO $$ooai:zaguan.unizar.es:169371$$particulos$$pdriver 000169371 951__ $$a2026-02-24-14:47:44 000169371 980__ $$aARTICLE