000135594 001__ 135594
000135594 005__ 20250214141228.0
000135594 0247_ $$2doi$$a10.1007/s11075-024-01843-7
000135594 0248_ $$2sideral$$a138714
000135594 037__ $$aART-2025-138714
000135594 041__ $$aeng
000135594 100__ $$0(orcid)0000-0002-6497-7158$$aKhiar, Y.$$uUniversidad de Zaragoza
000135594 245__ $$aOn the accurate computation of the Newton form of the Lagrange interpolant
000135594 260__ $$c2025
000135594 5060_ $$aAccess copy available to the general public$$fUnrestricted
000135594 5203_ $$aIn 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.
000135594 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-23R$$9info:eu-repo/grantAgreement/ES/DGA/S60-23R$$9info:eu-repo/grantAgreement/ES/MCIU/PID2022-138569NB-I00$$9info:eu-repo/grantAgreement/ES/MICINN/RED2022-134176-T
000135594 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000135594 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000135594 700__ $$0(orcid)0000-0002-1101-6230$$aMainar, E.$$uUniversidad de Zaragoza
000135594 700__ $$0(orcid)0000-0003-1550-8168$$aRoyo-Amondarain, E.$$uUniversidad de Zaragoza
000135594 700__ $$0(orcid)0000-0001-9130-0794$$aRubio, B.$$uUniversidad de Zaragoza
000135594 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000135594 773__ $$g98 (2025), 1553–1573$$pNumer. algorithms$$tNUMERICAL ALGORITHMS$$x1017-1398
000135594 8564_ $$s339470$$uhttps://zaguan.unizar.es/record/135594/files/texto_completo.pdf$$yVersión publicada
000135594 8564_ $$s1184251$$uhttps://zaguan.unizar.es/record/135594/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000135594 909CO $$ooai:zaguan.unizar.es:135594$$particulos$$pdriver
000135594 951__ $$a2025-02-14-14:11:23
000135594 980__ $$aARTICLE