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Mathematics of Computation

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Divided differences of implicit functions


Authors: Georg Muntingh and Michael Floater
Journal: Math. Comp. 80 (2011), 2185-2195
MSC (2010): Primary 26A24; Secondary 05A17, 41A05, 65D05
DOI: https://doi.org/10.1090/S0025-5718-2011-02486-5
Published electronically: April 12, 2011
MathSciNet review: 2813354
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Abstract: Under general conditions, the equation $ g(x,y) = 0$ implicitly defines $ y$ locally as a function of $ x$. In this article, we express divided differences of $ y$ in terms of bivariate divided differences of $ g$, generalizing a recent result on divided differences of inverse functions.


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Additional Information

Georg Muntingh
Affiliation: CMA/Matematisk Institutt, P.B 1053, Blindern, N-0316, Oslo, Norway
Email: georgmu@math.uio.no

Michael Floater
Affiliation: CMA/Matematisk Institutt, P.B 1053, Blindern, N-0316, Oslo, Norway
Email: michaelf@ifi.uio.no

DOI: https://doi.org/10.1090/S0025-5718-2011-02486-5
Received by editor(s): January 15, 2010
Received by editor(s) in revised form: September 24, 2010
Published electronically: April 12, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.