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9780898716597

Evaluating Derivatives

by ;
  • ISBN13:

    9780898716597

  • ISBN10:

    0898716594

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2008-09-26
  • Publisher: Society for Industrial & Applied

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Summary

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.

Table of Contents

Rules
Preface
Prologue
Mathematical symbols
Introduction
A framework for evaluating functions
Fundamentals of forward and reverse
Memory issues and complexity bounds
Repeating and extending reverse
Implementation and software
Sparse forward and reverse
Exploiting sparsity by compression
Going beyond forward and reverse
Jacobian and Hessian accumulation
Observations on efficiency
Reversal schedules and checkpointing
Taylor and tensor coefficients
Differentiation without differentiability
Implicit and iterative differentiation
Epilogue
List of figures
List of tables
Assumptions and definitions
Propositions, corollaries, and lemmas
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

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