TY - JOUR
T1 - On the Divided Difference Form of Faà di Bruno's Formula
JO - Journal of Computational Mathematics
VL - 4
SP - 553
EP - 560
PY - 2006
DA - 2006/08
SN - 24
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8774.html
KW - Divided difference, Newton interpolation, Composite function, Faà di Bruno's formula, Bell polynomial.
AB - <p style="text-align: justify;">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&#39;s formula of higher derivatives of function $h$.</p>