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Evaluating Derivatives

Evaluating Derivatives
Principles and Techniques of Algorithmic Differentiation

2nd Edition

£60.00

  • Date Published: November 2008
  • availability: Available in limited markets only
  • format: Paperback
  • isbn: 9780898716597

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  • 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.

    • 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
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    Product details

    • Edition: 2nd Edition
    • Date Published: November 2008
    • format: Paperback
    • isbn: 9780898716597
    • length: 460 pages
    • dimensions: 253 x 178 x 20 mm
    • weight: 0.81kg
    • availability: Available in limited markets only
  • 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.

  • Authors

    Andreas Griewank, Humboldt-Universität zu Berlin
    Andreas Griewank is a former senior scientist of Argonne National Laboratory and authored the first edition of this book in 2000. He holds a Ph.D. from the Australian National University and is currently Deputy Director of the Institute of Mathematics at Humboldt University Berlin and a member of the DFG Research Center Matheon, Mathematics for Key Technologies. His main research interests are nonlinear optimization and scientific computing.

    Andrea Walther, Technische Universität, Dresden
    Andrea Walther studied mathematics and economy at the University of Bayreuth. She holds a doctorate degree from the Technische Universität Dresden. Since 2003 Andrea Walther has been Juniorprofessor for the analysis and optimization of computer models at the Technische Universität Dresden. Her main research interests are scientific computing and nonlinear optimization.

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