Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: Michael S. Floater and Tom Lyche
Journal: Math. Comp. 76 (2007), 867-877
MSC (2000): Primary 05A17, 05A18, 26A06, 26A24, 41A05, 65D05
Published electronically: October 30, 2006
MathSciNet review: 2291840
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 05A17, 05A18, 26A06, 26A24, 41A05, 65D05

Retrieve articles in all journals with MSC (2000): 05A17, 05A18, 26A06, 26A24, 41A05, 65D05


Additional Information

Michael S. Floater
Affiliation: Centre of Mathematics for Applications, Department of Informatics, University of Oslo, PO Box 1053, Blindern, 0316 Oslo, Norway
Email: michaelf@ifi.uio.no

Tom Lyche
Affiliation: Centre of Mathematics for Applications, Department of Informatics, University of Oslo, PO Box 1053, Blindern, 0316 Oslo, Norway
Email: tom@ifi.uio.no

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01916-8
PII: S 0025-5718(06)01916-8
Keywords: Chain rule, divided differences, Fa{\`a} di Bruno's formula.
Received by editor(s): July 20, 2005
Published electronically: October 30, 2006
Article copyright: © Copyright 2006 American Mathematical Society