000128210 001__ 128210 000128210 005__ 20240122154817.0 000128210 0247_ $$2doi$$a10.1007/s11075-023-01588-9 000128210 0248_ $$2sideral$$a135359 000128210 037__ $$aART-2024-135359 000128210 041__ $$aeng 000128210 100__ $$0(orcid)0000-0002-1101-6230$$aMainar, E.$$uUniversidad de Zaragoza 000128210 245__ $$aHigh relative accuracy through Newton bases 000128210 260__ $$c2024 000128210 5060_ $$aAccess copy available to the general public$$fUnrestricted 000128210 5203_ $$aBidiagonal 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. 000128210 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/MCIU-AEI/PGC2018-096321-B-I00$$9info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T 000128210 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000128210 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000128210 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J.M.$$uUniversidad de Zaragoza 000128210 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, B.$$uUniversidad de Zaragoza 000128210 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000128210 773__ $$g95 (2024), 747–772$$pNumer. algorithms$$tNUMERICAL ALGORITHMS$$x1017-1398 000128210 8564_ $$s910062$$uhttps://zaguan.unizar.es/record/128210/files/texto_completo.pdf$$yVersión publicada 000128210 8564_ $$s1044597$$uhttps://zaguan.unizar.es/record/128210/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000128210 909CO $$ooai:zaguan.unizar.es:128210$$particulos$$pdriver 000128210 951__ $$a2024-01-22-15:43:57 000128210 980__ $$aARTICLE