EVALUATING DERIVATIVES. PRINCIPLES AND TECHNIQUES OF ALGORITHMIC DIFFERENTIATION. 2ND EDITION

Rules
Preface
Prologue
Mathematical symbols
1. Introduction
2. A framework for evaluating functions
3. Fundamentals of forward and reverse
4. Memory issues and complexity bounds
5. Repeating and extending reverse
6. Implementation and software
7. Sparse forward and reverse
8. Exploiting sparsity by compression
9. Going beyond forward and reverse
10. Jacobian and Hessian accumulation
11. Observations on efficiency
12. Reversal schedules and checkpointing
13. Taylor and tensor coefficients
14. Differentiation without differentiability
15. Implicit and iterative differentiation
Epilogue
List of figures
List of tables
Assumptions and definitions
Propositions, corollaries, and lemmas
Bibliography
Index.

Algorithmic, or automatic, differentiation (AD) is a growing area of theoretical research and software development concerned with the accurate and efficient evaluation of derivatives for function evaluations given as computer programs. The resulting derivative values are useful for all scientific computations that are based on linear, quadratic, or higher order approximations to nonlinear scalar or vector functions. This second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity. There is also added material on checkpointing and iterative differentiation. To improve readability the more detailed analysis of memory and complexity bounds has been relegated to separate, optional chapters. The book consists of: a stand-alone introduction to the fundamentals of AD and its software; a thorough treatment of methods for sparse problems; and final chapters on program-reversal schedules, higher derivatives, nonsmooth problems and iterative processes.

Features
• Each chapter concludes with examples and exercises
• Updated and expanded to cover recent developments in applications and theory
• Provides the insight necessary to choose and deploy existing AD software tools to the best advantage