On the efficient computation of high-order derivatives for implicitly defined functions
Dec, 2009
Citations per year
Abstract: (arXiv)
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.- 02.60.Gf
- 12.38.Aw
- 02.70.Bf
- 11.30.Rd
- Algorithmic differentiation
- Numerical differentiation
- Taylor expansion
- Quantum chromodynamics
- derivative: high
- sigma model: linear
References(13)
Figures(0)