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000078093 005__ 20200716101512.0
000078093 0247_ $$2doi$$a10.1016/j.jat.2017.07.005
000078093 0248_ $$2sideral$$a110367
000078093 037__ $$aART-2019-110367
000078093 041__ $$aeng
000078093 100__ $$0(orcid)0000-0003-4359-1499$$aCarnicer, J.M.$$uUniversidad de Zaragoza
000078093 245__ $$aOptimal stability of the Lagrange formula and conditioning of the Newton formula
000078093 260__ $$c2019
000078093 5060_ $$aAccess copy available to the general public$$fUnrestricted
000078093 5203_ $$aA pointwise condition number associated to a representation of an interpolation operator is introduced. It is proved that the Lagrange formula is optimal with respect to this conditioning. For other representations of the interpolation operator, an upper bound for the conditioning is derived. A quantitative measure in terms of the Skeel condition number is used to compare the conditioning with the Lagrange representation. The conditioning of the Newton representation is considered for increasing nodes and for nodes in Leja order. For the polynomial Newton formula with n+1 equidistant nodes in increasing order, it is proved that 3n is the best uniform bound of its conditioning and it is attained at the last node. Numerical experiments are included.
000078093 536__ $$9info:eu-repo/grantAgreement/ES/DGA/FSE$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65433-P
000078093 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000078093 590__ $$a0.825$$b2019
000078093 591__ $$aMATHEMATICS$$b155 / 324 = 0.478$$c2019$$dQ2$$eT2
000078093 592__ $$a0.663$$b2019
000078093 593__ $$aAnalysis$$c2019$$dQ2
000078093 593__ $$aNumerical Analysis$$c2019$$dQ2
000078093 593__ $$aMathematics (miscellaneous)$$c2019$$dQ2
000078093 593__ $$aApplied Mathematics$$c2019$$dQ2
000078093 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000078093 700__ $$0(orcid)0000-0002-6497-7158$$aKhiar, Y.$$uUniversidad de Zaragoza
000078093 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J.M.$$uUniversidad de Zaragoza
000078093 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000078093 773__ $$g238 (2019), 52-66$$pJ. approx. theory$$tJournal of Approximation Theory$$x0021-9045
000078093 8564_ $$s265565$$uhttps://zaguan.unizar.es/record/78093/files/texto_completo.pdf$$yPostprint
000078093 8564_ $$s52036$$uhttps://zaguan.unizar.es/record/78093/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
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000078093 951__ $$a2020-07-16-09:19:37
000078093 980__ $$aARTICLE