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On the Efficient Evaluation of Higher-Order Derivatives of Real-Valued Functions Composed of Matrix Operations

In: Modeling, Simulation and Optimization of Complex Processes

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  • Sebastian F. Walter

    (Humboldt-Universität zu Berlin, Department of Mathematics, Faculty of Mathematics and Natural Sciences II)

Abstract

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.

Suggested Citation

  • Sebastian F. Walter, 2012. "On the Efficient Evaluation of Higher-Order Derivatives of Real-Valued Functions Composed of Matrix Operations," Springer Books, in: Hans Georg Bock & Xuan Phu Hoang & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes, edition 127, pages 315-324, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25707-0_26
    DOI: 10.1007/978-3-642-25707-0_26
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