Optimal stability of the Lagrange formula and conditioning of the Newton formula

Carnicer, J.M. (Universidad de Zaragoza) ; Khiar, Y. (Universidad de Zaragoza) ; Peña, J.M. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.jat.2017.07.005

Año: 2019

Publicado en: Journal of Approximation Theory 238 (2019), 52-66
ISSN: 0021-9045

Factor impacto JCR: 0.825 (2019)

Categ. JCR: MATHEMATICS rank: 155 / 324 = 0.478 (2019) - Q2 - T2

Factor impacto SCIMAGO: 0.663 - Analysis (Q2) - Numerical Analysis (Q2) - Mathematics (miscellaneous) (Q2) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/FSE
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65433-P

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)