135594 20250214141228.0 doi 10.1007/s11075-024-01843-7 sideral 138714 ART-2025-138714 eng Khiar, Y. Universidad de Zaragoza (orcid)0000-0002-6497-7158 On the accurate computation of the Newton form of the Lagrange interpolant 2025 Access copy available to the general public Unrestricted In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great precision, even for large ill-conditioned matrices. In this framework, the present work provides the factorization of the collocation matrices of Newton bases—of relevance when considering the Lagrange interpolation problem—together with an algorithm that allows to numerically compute it to high relative accuracy. This further allows to determine the coefficients of the interpolating polynomial and to compute the singular values and the inverse of the collocation matrix. Conditions that guarantee high relative accuracy for these methods and, in the former case, for the classical recursion formula of divided differences, are determined. Numerical errors due to imprecise computer arithmetic or perturbed input data in the computation of the factorization are analyzed. Finally, numerical experiments illustrate the accuracy and effectiveness of the proposed methods with several algebraic problems, in stark contrast with traditional approaches. info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/DGA/S60-23R info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00 info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Mainar, E. Universidad de Zaragoza (orcid)0000-0002-1101-6230 Royo-Amondarain, E. Universidad de Zaragoza (orcid)0000-0003-1550-8168 Rubio, B. Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 98 (2025), 1553–1573 Numer. algorithms NUMERICAL ALGORITHMS 1017-1398 339470 http://zaguan.unizar.es/record/135594/files/texto_completo.pdf Versión publicada 1184251 http://zaguan.unizar.es/record/135594/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:135594 articulos driver 2025-02-14-14:11:23 ARTICLE