Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the efficient computation of high-order derivatives for implicitly
  defined functions   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.

35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat