Year: 2006
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 4 : pp. 553–560
Abstract
The $n$-divided difference of the composite function $h:=f\circ g$ of functions $f$, $g$ at a group of nodes $t_0, t_1, \cdots, t_n$ is shown by the combinations of divided differences of $f$ at the group of nodes $g(t_0), g(t_1), \cdots, g(t_m)$ and divided differences of $g$ at several partial group of nodes $t_0, t_1,\cdots, t_n$, where $m=1, 2,\cdots, n$. Especially, when the given group of nodes are equal to each other completely, it will lead to Faà di Bruno's formula of higher derivatives of function $h$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8774
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 4 : pp. 553–560
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Divided difference Newton interpolation Composite function Faà di Bruno's formula Bell polynomial.