Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs. No truncation errors are incurred, and the resulting numerical derivative values can be used for all scientific computations that are based on linear, quadratic, or even higher order approximations to nonlinear scalar or vector functions. In particular, AD has been applied to optimization, parameter identification, equation solving, the numerical integration of differential equations, and combinations thereof. Apart from quantifying sensitivities numerically, AD techniques can also provide structural information, e.g., sparsity pattern and generic rank of Jacobian matrices.
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Book Description
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Editorial Reviews
Book Description
The book is divided into three parts: a stand-alone introduction to the fundamentals of AD and its software, a thorough treatment of methods for sparse problems, and final chapters on higher derivatives, nonsmooth problems, and program reversal schedules.
From the Publisher
This volume will be valuable for designers and users of algorithms and software for nonlinear computational problems. It opens up an exciting opportunity to develop new algorithms that reflect the availability of accurate derivatives and their true cost to achieve improvements in speed and reliability. Some familiarity with modern approaches to the seemingly straightforward task of evaluating derivatives will benefit any mathematician, scientist or engineer.
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Inside This Book
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First Sentence:
As demonstrated by the above quote, the basic idea behind the differentiation methodology explored in this book is by no means new. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonincremental form, adjoint procedure, adjoint recursion, adjoint sensitivity equation, reversal schedule, elemental partials, linearized computational graph, tangent procedure, split reversal, basic reverse mode, adjoint values, joint reversal, derivative recurrence, runtime ratio, partial separability, row compression, value separability, tree reversal, runtime functional, returning motion, lighthouse problem, univariate taylor series, adjoint components, argument separability, elemental functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Temporal Complexity Model, Sparse Second Derivatives New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
As demonstrated by the above quote, the basic idea behind the differentiation methodology explored in this book is by no means new. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonincremental form, adjoint procedure, adjoint recursion, adjoint sensitivity equation, reversal schedule, elemental partials, linearized computational graph, tangent procedure, split reversal, basic reverse mode, adjoint values, joint reversal, derivative recurrence, runtime ratio, partial separability, row compression, value separability, tree reversal, runtime functional, returning motion, lighthouse problem, univariate taylor series, adjoint components, argument separability, elemental functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Temporal Complexity Model, Sparse Second Derivatives New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
19
books
cite this book:
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- Automatic Differentiation of Algorithms by George Corliss in Back Matter (1), and Back Matter (2)
- Global Optimization and Constraint Satisfaction: First International Workshop Global Constraint Optimization and Constraint Satisfaction, COCOS 2002, ... Papers (Lecture Notes in Computer Science) by Christian Bliek on page 30
- Online Optimization of Large Scale Systems: State of the Art by Martin Grötschel on page 334
- Computational Approaches for Aerospace Design: The Pursuit of Excellence by Prof. Andy Keane in Back Matter
- Nonlinear Equations and Optimisation, Volume 4 (Numerical Analysis 2000) by L.T. Watson on page 190
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