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

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 Faà di Bruno's formula and other formulas for higher derivatives...

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Bibliographic Details
Published in:Mathematics of computation 2007-04, Vol.76 (258), p.867-877
Main Authors: Floater, Michael S., Lyche, Tom
Format: Article
Language:English
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Summary: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 Faà di Bruno's formula and other formulas for higher derivatives of composite functions. We also derive a divided difference version of Faà di Bruno's determinant formula.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-06-01916-8