Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 15 (2020), 257 -- 279

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ON HERMITE INTERPOLATION AND DIVIDED DIFFERENCES

François Dubeau

Abstract. This paper is a survey of topics related to Hermite interpolation. In the first part we present the standard analysis of the Hermite interpolation problem. Existence, uniqueness and error formula are included. Then some computational aspects are studied including Leibnitz' formula and devided differences for monomials. Moreover continuity and differentiation properties of divided differences are analyzed. Finally we represent Hermite polynomial with respect to different basis and give links between them.

2020 Mathematics Subject Classification: 41A05; 65D05; 26C99
Keywords: Hermite interpolation; Hermite interpolating polynomial; divided differences; Leibnitz' formula; monomials; representation of Hermite polynomial

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François Dubeau
Département de mathématiques,
Faculté des sciences, Université de Sherbrooke,
2500, boul. de l'Université,
Sherbrooke (Qc), Canada, J1K 2R1.
e-mail: francois.dubeau@usherbrooke.ca
https://www.usherbrooke.ca/mathematiques/personnel/corps-professoral/professeurs/francois-dubeau/

http://www.utgjiu.ro/math/sma