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Evaluating higher derivative tensors by forward propagation of univariate Taylor series

Authors: Andreas Griewank, Jean Utke and Andrea Walther
Journal: Math. Comp. 69 (2000), 1117-1130
MSC (1991): Primary 65D05, 65Y20, 68Q40
Published electronically: February 17, 2000
MathSciNet review: 1651755
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Abstract | References | Similar Articles | Additional Information


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.

References [Enhancements On Off] (What's this?)

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Additional Information

Andreas Griewank
Affiliation: Institute of Scientific Computing, Technical University Dresden, D-01062 Dresden, Germany

Jean Utke
Affiliation: Framework Technologies, Inc., 10 South Riverside Plaza, Suite 1800, Chicago, Illinois 60606

Andrea Walther
Affiliation: Institute of Scientific Computing, Technical University Dresden, D-01062 Dresden, Germany

Keywords: Higher order derivatives, computational differentiation
Received by editor(s): January 2, 1998
Received by editor(s) in revised form: June 30, 1998
Published electronically: February 17, 2000
Additional Notes: This work was partially supported by the Deutsche Forschungsgesellschaft under grant GR 705/4-1.
Article copyright: © Copyright 2000 American Mathematical Society