Evaluating derivatives. Principles and techniques of algorithmic differentiation. 2nd ed.

*(English)*Zbl 1159.65026
Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-59-7/pbk; 978-0-89871-776-1/ebook). xxi, 438 p. (2008).

The monograph is the second edition of a book that appeared in 2000 [Evaluating derivatives. Principles and techniques of algorithmic differentiation, Philadelphia, PA: SIAM (2000; Zbl 0958.65028)]. It presents a very well-written and comprehensive introduction to algorithmic differentiation (AD) which is concerned with the accurate and efficient evaluation for derivatives for functions given by computer programs. The second edition has been updated and expanded to cover recent developments, including the NP completeness of optimal Jacobian accumulation and an introduction to scarcity, a generalization of sparsity. There is also added material on checkpointing and iterative differentiation. The analysis of memory and complexity bounds is now handled in a separate chapter.

This book consists of three parts (with 15 chapters). The first part “Tangents and gradients” is a stand-alone introduction to the fundamentals of AD and its software. The second part “Jacobians and Hessians” is a comprehensive treatment for sparse problems. The final part “Advances and reversals” deals with program-reversal schedules, higher derivatives, nonsmooth problems, and iterative processes. Each chapter ends with several exercises.

This monograph will be very valuable for graduate students, mathematicians, and engineers who are interested in the design of efficient algorithms for nonlinear problems. It will stimulate the further research in AD.

This book consists of three parts (with 15 chapters). The first part “Tangents and gradients” is a stand-alone introduction to the fundamentals of AD and its software. The second part “Jacobians and Hessians” is a comprehensive treatment for sparse problems. The final part “Advances and reversals” deals with program-reversal schedules, higher derivatives, nonsmooth problems, and iterative processes. Each chapter ends with several exercises.

This monograph will be very valuable for graduate students, mathematicians, and engineers who are interested in the design of efficient algorithms for nonlinear problems. It will stimulate the further research in AD.

Reviewer: Manfred Tasche (Rostock)

##### MSC:

65D25 | Numerical differentiation |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65F50 | Computational methods for sparse matrices |

68W30 | Symbolic computation and algebraic computation |