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Erschienen in:
2012 | OriginalPaper | Buchkapitel
On the Efficient Evaluation of Higher-Order Derivatives of Real-Valued Functions Composed of Matrix Operations
verfasst von : Sebastian F. Walter
Erschienen in: Modeling, Simulation and Optimization of Complex Processes
Verlag: Springer Berlin Heidelberg
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Two different hierarchical levels of algorithmic differentiation are compared: the traditional approach and a higher-level approach where matrix operations are considered to be atomic. More explicitly: It is discussed how computer programs that consist of matrix operations (e.g. matrix inversion) can be evaluated in univariate Taylor polynomial arithmetic. Formulas suitable for the reverse mode are also shown. The advantages of the higher-level approach are discussed, followed by an experimental runtime comparison.