On the efficient computation of high-order derivatives for implicitly defined functions

Details On the efficient computation of high-order derivatives for implicitly defined functions On the efficient computation of high-order derivatives for implicitly defined functions

2009-12-11

arxiv.org/abs/0912.2208v1

Comput.Phys.Commun.181:756-764,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

11 pages, 4 figures, to appear in Comput. Phys. Commun

Scientific paper

10.1016/j.cpc.2009.12.008

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order derivatives. A technique based on algorithmic differentiation is presented which allows for a precise calculation of higher-order derivatives. The method can be widely applied even for the case of only numerically solvable, implicit dependencies which totally hamper a semi-analytical calculation of the derivatives. As a demonstration the method is applied to a quantum field theoretical physical model. The results are compared with standard numerical derivative methods.

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