Advances in Automatic Differentiation (Lecture Notes in Computational Science and Engineering)

✍ Scribed by Christian H. Bischof, H. Martin Bücker, Paul Hovland, Uwe Naumann, Jean Utke

• Year: 2008
• Tongue: English
• Leaves: 366
• Edition: 1
• Category: Library

✦ Synopsis

This collection covers advances in automatic differentiation theory and practice. Computer scientists and mathematicians will learn about recent developments in automatic differentiation theory as well as mechanisms for the construction of robust and powerful automatic differentiation tools. Computational scientists and engineers will benefit from the discussion of various applications, which provide insight into effective strategies for using automatic differentiation for inverse problems and design optimization.

✦ Table of Contents

Contents......Page 8
Preface......Page 5
List of Contributors......Page 11
Reverse Automatic Differentiation of Linear Multistep Methods......Page 17
Call Tree Reversal is NP-Complete......Page 29
On Formal Certification of AD Transformations......Page 39
Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation......Page 50
A Modification of Weeks' Method for Numerical Inversion of the Laplace Transform in the Real Case Based on Automatic Differentiation......Page 60
A Low Rank Approach to Automatic Differentiation......Page 70
Algorithmic Differentiation of Implicit Functions and Optimal Values......Page 81
Using Programming Language Theory to Make Automatic Differentiation Sound and Efficient......Page 92
A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs......Page 104
On the Practical Exploitation of Scarsity......Page 116
Design and Implementation of a Context-Sensitive, Flow-Sensitive Activity Analysis Algorithm for Automatic Differentiation......Page 128
Efficient Higher-Order Derivatives of the Hypergeometric Function......Page 139
The Diamant Approach for an Efficient Automatic Differentiationof the Asymptotic Numerical Method......Page 150
Tangent-on-Tangent vs. Tangent-on-Reverse for Second Differentiation of Constrained Functionals......Page 161
Parallel Reverse Mode Automatic Differentiation for OpenMP Programs with ADOL-C......Page 172
Adjoints for Time-Dependent Optimal Control......Page 183
Development and First Applications of TAC++......Page 194
TAPENADE for C......Page 205
Coping with a Variable Number of Arguments when Transforming MATLAB Programs......Page 216
Code Optimization Techniques in Source Transformations for Interpreted Languages......Page 228
Automatic Sensitivity Analysis of DAE-systems Generated from Equation-Based Modeling Languages......Page 239
Index Determination in DAEs Using the Library indexdet and the ADOL-C Package for Algorithmic Differentiation......Page 251
Automatic Differentiation for GPU-Accelerated 2D/3D Registration......Page 262
Robust Aircraft Conceptual Design Using Automatic Differentiation in Matlab......Page 273
Toward Modular Multigrid Design Optimisation......Page 283
Large Electrical Power Systems Optimization Using Automatic Differentiation......Page 294
On the Application of Automatic Differentiation to the Likelihood Function for Dynamic General Equilibrium Models......Page 304
Combinatorial Computation with Automatic Differentiation......Page 315
Exploiting Sparsity in Jacobian Computation via Coloring and Automatic Differentiation: A Case Study in a Simulated Moving Bed Process......Page 326
Structure-Exploiting Automatic Differentiation of Finite Element Discretizations......Page 338
Large-Scale Transient Sensitivity Analysis of a Radiation-Damaged Bipolar Junction Transistor via Automatic Differentiation......Page 349

✦ Subjects

Математика;Вычислительная математика;