Second Order Differentiation Formula in a Computational Graph

8 Pages Posted: 25 Jan 2017 Last revised: 24 Nov 2017

Date Written: January 24, 2017

Abstract

F. L. Bauer expressed a first order differentiation closed formula in a computational graph based on the multivariate chain rule. We propose and prove in this article a similarly closed formula for second order derivative.

We analyse the complexity of those two formulas and prove that, in certain cases, it is exponential with respect to the number of vertices in the computational graph.

Keywords: bauer, computational, graph, derivative, second, order, first, differentiation, chain, rule

JEL Classification: C63

Suggested Citation

Duche, Henri-Olivier and Galilee, Francois, Second Order Differentiation Formula in a Computational Graph (January 24, 2017). Available at SSRN: https://ssrn.com/abstract=2905103 or http://dx.doi.org/10.2139/ssrn.2905103

Henri-Olivier Duche (Contact Author)

Independent ( email )

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Francois Galilee

Independent ( email )

No Address Available

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