Two chain rules for divided differences and Faa di Bruno's formula

被引：20
|
作者：
Floater, Michael S. [1 ]
Lyche, Tom [1 ]
机构：
[1] Univ Oslo, Dept Informat, Ctr Math Applicat, N-0316 Oslo, Norway
来源：
MATHEMATICS OF COMPUTATION | 2007年 / 76卷 / 258期
关键词：
chain rule; divided differences; Faa di Bruno's formula;
D O I：
10.1090/S0025-5718-06-01916-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we derive two formulas for divided differences of a function of a function. Both formulas lead to other divided difference formulas, such as reciprocal and quotient rules. The two formulas can also be used to derive Faa di Bruno's formula and other formulas for higher derivatives of composite functions. We also derive a divided difference version of Faa di Bruno's determinant formula.
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页码：867 / 877
页数：11
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