Divided differences of implicit functions

Muntingh, Georg; Floater, Michael

doi:10.1090/S0025-5718-2011-02486-5

Divided differences of implicit functions
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by Georg Muntingh and Michael Floater;

Math. Comp. 80 (2011), 2185-2195

DOI: https://doi.org/10.1090/S0025-5718-2011-02486-5

Published electronically: April 12, 2011

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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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