151712 20251017144640.0 doi 10.3934/math.2025178 sideral 143188 ART-2025-143188 eng Khiar, Yasmina Universidad de Zaragoza (orcid)0000-0002-6497-7158 High relative accuracy for a Newton form of bivariate interpolation problems 2025 Access copy available to the general public Unrestricted The problem of bivariate polynomial interpolation using Newton-type bases is examined, leading to the application of a generalized Kronecker matrix product. Algorithms for computing the coefficients of the interpolating polynomial are presented, along with conditions that ensure relative errors of the order of machine precision. A generalization of the classical recursion formula of divided differences in two dimensions is proposed for grids that generalize the standard rectangular layout. Numerical experiments demonstrate the high accuracy achieved by the proposed approach. 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 Mainar, Esmeralda Universidad de Zaragoza (orcid)0000-0002-1101-6230 Royo-Amondarain, Eduardo Universidad de Zaragoza (orcid)0000-0003-1550-8168 Rubio, Beatriz Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 10, 2 (2025), 3836-3847 AIMS Mathematics 2473-6988 252748 http://zaguan.unizar.es/record/151712/files/texto_completo.pdf Versión publicada 2004528 http://zaguan.unizar.es/record/151712/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:151712 articulos driver 2025-10-17-14:31:25 ARTICLE