169371 20260225105429.0 doi 10.1007/s10092-026-00683-2 sideral 148320 ART-2026-148320 eng Díaz, Pablo Universidad de Zaragoza Perturbation theory and error analysis for the Cauchy formula 2026 In 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. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00 info:eu-repo/grantAgreement/ES/MCIU/RED2022-134176-T info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Khiar, Yasmina Universidad de Zaragoza (orcid)0000-0002-6497-7158 Mainar, Esmeralda Universidad de Zaragoza (orcid)0000-0002-1101-6230 Royo-Amondarain, Eduardo Universidad de Zaragoza (orcid)0000-0003-1550-8168 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 63, 1 (2026), [17 pp.] Calcolo CALCOLO 0008-0624 3434954 http://zaguan.unizar.es/record/169371/files/texto_completo.pdf Versión publicada 959322 http://zaguan.unizar.es/record/169371/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:169371 articulos driver 2026-02-24-14:47:44 ARTICLE