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Zbl 0958.65028
Griewank, Andreas
Evaluating derivatives. Principles and techniques of algorithmic differentiation. (English)
[B] Frontiers in Applied Mathematics. 19. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xxiv, 369 p. \$ 49.50 (2000). ISBN 0-89871-451-6

Frequently, numerical values for a composite function are calculated by a program. Algorithmic, or automatic differentiation (AD) is concerned with the efficient and accurate evaluation of derivatives for such function. The resulting derivatives can be used in numerous algorithms for nonlinear problems. \par The new book is written by a specialist in AD and presents a comprehensive treatment of AD. Earlier textbooks on AD [cf. {\it L. Rall}, Automatic differentiation: Techniques and applications (1981; Zbl 0473.68025) and {\it H. Kagiwada}, {\it R. Kalaba}, {\it N. Rasakhoo} and {\it K. Spingarn}, Numerical derivatives and nonlinear analysis (1986; Zbl 0665.65017)], cover only the forward mode of AD. The book under review describes all chain-rule based techniques for evaluating derivatives of composite functions with emphasis on the reverse mode. The computation of gradients is always cheap, while the cost of evaluating Jacobian and Hessian matrices depends on the problem structure and its efficient exploitation. Attempts to minimize operations count and memory requirement lead to hard combinatorial optimization problems. \par This book is divided into three parts.\newl Part I (with Chapters 2-5) presents an introduction to the fundamentals of AD and its software. In general, Jacobian and Hessian matrices cannot be obtained cheaply. \newl Part II (with Chapters 6-9) examines the typical situation, where Jacobians and Hessians are sparse or structured, such that they can be computed cheaply by matrix compression.\newl Part III (with Chapters 10 - 12) contains more advanced material (very large problems, higher derivatives, generalized gradients, differentiation of codes with nondifferentiabilities) which will be of interest mostly to researchers. \par Each chapter concludes with many examples and exercises suitable also for students with a basic knowledge of calculus, procedural programming, and numerical linear algebra.\par This well written book will be very useful for graduate students, mathematicians and engineers, who are interested in efficient algorithms for nonlinear problems.
[Manfred Tasche (Rostock)]

MSC 2000:: *65D25 Numerical differentiation
65-02 Research monographs (numerical analysis)
65F50 Sparse matrices
68-02 Research monographs (computer science)
68W30 Symbolic computation and algebraic computation

Keywords: algorithmic differentiation; automatic differentiation; forward mode; reverse mode; computation of gradients; matrix compression; software; monograph; structured matrices; Jacobian matrix; Hessian matrix; sparse matrices; algorithms; combinatorial optimization; examples; exercises

Citations: Zbl 0473.68025; Zbl 0665.65017

Cited in: Zbl 1159.65026 Zbl 1218.01018 Zbl 1134.15301

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