Advances in Automatic Differentiation

ISBN: 978-3-540-68935-5 (Print) 978-3-540-68942-3 (Online)

Table of contents (31 chapters)

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  1. Front Matter

    Pages I-XVIII

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    Book Chapter

    Pages 1-12

    Reverse Automatic Differentiation of Linear Multistep Methods

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    Book Chapter

    Pages 13-22

    Call Tree Reversal is NP-Complete

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    Book Chapter

    Pages 23-33

    On Formal Certification of AD Transformations

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    Book Chapter

    Pages 35-44

    Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation

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    Book Chapter

    Pages 45-54

    A Modification of Weeks’ Method for Numerical Inversion of the Laplace Transform in the Real Case Based on Automatic Differentiation

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    Book Chapter

    Pages 55-65

    A Low Rank Approach to Automatic Differentiation

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    Book Chapter

    Pages 67-77

    Algorithmic Differentiation of Implicit Functions and Optimal Values

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    Book Chapter

    Pages 79-90

    Using Programming Language Theory to Make Automatic Differentiation Sound and Efficient

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    Book Chapter

    Pages 91-102

    A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs

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    Book Chapter

    Pages 103-114

    On the Practical Exploitation of Scarsity

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    Book Chapter

    Pages 115-125

    Design and Implementation of a Context-Sensitive, Flow-Sensitive Activity Analysis Algorithm for Automatic Differentiation

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    Book Chapter

    Pages 127-137

    Efficient Higher-Order Derivatives of the Hypergeometric Function

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    Book Chapter

    Pages 139-149

    The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method

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    Book Chapter

    Pages 151-161

    Tangent-on-Tangent vs. Tangent-on-Reverse for Second Differentiation of Constrained Functionals

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    Book Chapter

    Pages 163-173

    Parallel Reverse Mode Automatic Differentiation for OpenMP Programs with ADOL-C

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    Book Chapter

    Pages 175-185

    Adjoints for Time-Dependent Optimal Control

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    Book Chapter

    Pages 187-197

    Development and First Applications of TAC++

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    Book Chapter

    Pages 199-209

    TAPENADE for C

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    Book Chapter

    Pages 211-222

    Coping with a Variable Number of Arguments when Transforming MATLAB Programs

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    Book Chapter

    Pages 223-233

    Code Optimization Techniques in Source Transformations for Interpreted Languages

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