Evaluating Derivatives
Evaluating Derivatives
Andrea Walther , Technische Universität, Dresden
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USDAlgorithmic, 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.
- 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
Product details
November 2008Paperback
9780898716597
460 pages
253 × 178 × 20 mm
0.81kg
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
- 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.
