78093 20200716101512.0 doi 10.1016/j.jat.2017.07.005 sideral 110367 ART-2019-110367 eng (orcid)0000-0003-4359-1499 Carnicer, J.M. Universidad de Zaragoza Optimal stability of the Lagrange formula and conditioning of the Newton formula 2019 Access copy available to the general public Unrestricted A 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. info:eu-repo/grantAgreement/ES/DGA/FSE info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65433-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.825 2019 MATHEMATICS 155 / 324 = 0.478 2019 Q2 T2 0.663 2019 Analysis 2019 Q2 Numerical Analysis 2019 Q2 Mathematics (miscellaneous) 2019 Q2 Applied Mathematics 2019 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0002-6497-7158 Khiar, Y. Universidad de Zaragoza (orcid)0000-0002-1340-0666 Peña, J.M. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 238 (2019), 52-66 J. approx. theory Journal of Approximation Theory 0021-9045 265565 http://zaguan.unizar.es/record/78093/files/texto_completo.pdf Postprint 52036 http://zaguan.unizar.es/record/78093/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:78093 articulos driver 2020-07-16-09:19:37 ARTICLE