Evaluating Derivatives – Principles and Techniques of Algorithmic Differentiation

TRAMA

This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity. There is also added material on checkpointing and iterative differentiation.

NOTE EDITORE

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.

SOMMARIO

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.

PREFAZIONE

A comprehensive treatment of algorithmic, or automatic, differentiation for designers of algorithms and software for nonlinear computational problems, users of current numerical software, mathematicians, and engineers. This second edition has been updated and expanded to cover recent developments in applications and theory.

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780898716597
• Dimensioni: 229 x 19.5 x 152 mm Ø 982 gr
• Formato: Brossura
• Pagine Arabe: 460