an:01449984
Zbl 0952.65028
Griewank, Andreas; Utke, Jean; Walther, Andrea
Evaluating higher derivative tensors by forward propagation of univariate Taylor series
EN
Math. Comput. 69, No. 231, 1117-1130 (2000).
00065939
2000
j
65D25 65F30 68W30 65Y20 65T99
higher order derivatives; computational differentiation; tensors; function of several variables; partial derivatives; computational complexities
The paper describes a new approach to compute higher order derivatives of a function of several variables. The approach is based on the calculation of one-dimensional Taylor developments of the function along conveniently selected directions, i.e. directional Taylor developments. The directions are given by the lattice points of nonnegative integers whose coordinates add up to a fixed derivative order. It is shown that those developments allow to interpolate all the partial derivatives whose degrees are smaller or equal than the order considered initially.
The paper includes a discussion and estimates of the computational complexities, such as data structures and memory access pattern, as well as some time run results, which show that the proposed approach can be useful in applications that require the calculation of higher order derivatives in several variables.
Juan Pedro Milaszewicz (Buenos Aires)