128210 20260217205515.0 doi 10.1007/s11075-023-01588-9 sideral 135359 ART-2024-135359 eng Mainar, E. Universidad de Zaragoza (orcid)0000-0002-1101-6230 High relative accuracy through Newton bases 2024 Access copy available to the general public Unrestricted Bidiagonal factorizations for the change of basis matrices between monomial and Newton polynomial bases are obtained. The total positivity of these matrices is characterized in terms of the sign of the nodes of the Newton bases. It is shown that computations to high relative accuracy for algebraic problems related to these matrices can be achieved whenever the nodes have the same sign. Stirling matrices can be considered particular cases of these matrices, and then computations to high relative accuracy for collocation and Wronskian matrices of Touchard polynomial bases can be obtained. The performed numerical experimentation confirms the accurate solutions obtained when solving algebraic problems using the proposed factorizations, for instance, for the calculation of their eigenvalues, singular values, and inverses, as well as the solution of some linear systems of equations associated with these matrices. info:eu-repo/grantAgreement/ES/DGA/E41-23R info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00 info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 2.0 2024 MATHEMATICS, APPLIED 65 / 344 = 0.189 2024 Q1 T1 0.859 2024 Applied Mathematics 2024 Q1 3.9 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Peña, J.M. Universidad de Zaragoza (orcid)0000-0002-1340-0666 Rubio, B. Universidad de Zaragoza (orcid)0000-0001-9130-0794 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 95 (2024), 747–772 Numer. algorithms NUMERICAL ALGORITHMS 1017-1398 910062 http://zaguan.unizar.es/record/128210/files/texto_completo.pdf Versión publicada 1044597 http://zaguan.unizar.es/record/128210/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:128210 articulos driver 2026-02-17-20:26:34 ARTICLE