Journal
MATHEMATICS OF COMPUTATION
Volume 69, Issue 231, Pages 1117-1130Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-00-01120-0
Keywords
higher order derivatives; computational differentiation
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This article considers the problem of evaluating all pure and mixed partial derivatives of some vector function defined by an evaluation procedure. The natural approach to evaluating derivative tensors might appear to be their recursive calculation in the usual forward mode of computational differentiation. However, with the approach presented in this article, much simpler data access patterns and similar or lower computational counts can be achieved through propagating a family of univariate Taylor series of a suitable degree. It is applicable for arbitrary orders of derivatives. Also it is possible to calculate derivatives only in some directions instead of the full derivative tensor. Explicit formulas for all tensor entries as well as estimates for the corresponding computational complexities are given.
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