The Art of Differentiating Computer Programs

The Art of Differentiating Computer Programs
Title The Art of Differentiating Computer Programs PDF eBook
Author Uwe Naumann
Publisher SIAM
Pages 358
Release 2012-01-01
Genre Mathematics
ISBN 9781611972078

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This is the first entry-level book on algorithmic (also known as automatic) differentiation (AD), providing fundamental rules for the generation of first- and higher-order tangent-linear and adjoint code. The author covers the mathematical underpinnings as well as how to apply these observations to real-world numerical simulation programs. Readers will find: examples and exercises, including hints to solutions; the prototype AD tools dco and dcc for use with the examples and exercises; first- and higher-order tangent-linear and adjoint modes for a limited subset of C/C++, provided by the derivative code compiler dcc; a supplementary website containing sources of all software discussed in the book, additional exercises and comments on their solutions (growing over the coming years), links to other sites on AD, and errata.

Automatic Differentiation

Automatic Differentiation
Title Automatic Differentiation PDF eBook
Author Louis B. Rall
Publisher Springer
Pages 194
Release 1981
Genre Mathematics
ISBN

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Advances in Automatic Differentiation

Advances in Automatic Differentiation
Title Advances in Automatic Differentiation PDF eBook
Author Christian H. Bischof
Publisher Springer Science & Business Media
Pages 366
Release 2008-08-17
Genre Computers
ISBN 3540689427

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The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic “silver bullet” polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

Automatic Differentiation of Algorithms

Automatic Differentiation of Algorithms
Title Automatic Differentiation of Algorithms PDF eBook
Author George Corliss
Publisher Springer Science & Business Media
Pages 431
Release 2013-11-21
Genre Computers
ISBN 1461300754

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A survey book focusing on the key relationships and synergies between automatic differentiation (AD) tools and other software tools, such as compilers and parallelizers, as well as their applications. The key objective is to survey the field and present the recent developments. In doing so the topics covered shed light on a variety of perspectives. They reflect the mathematical aspects, such as the differentiation of iterative processes, and the analysis of nonsmooth code. They cover the scientific programming aspects, such as the use of adjoints in optimization and the propagation of rounding errors. They also cover "implementation" problems.

Evaluating Derivatives

Evaluating Derivatives
Title Evaluating Derivatives PDF eBook
Author Andreas Griewank
Publisher SIAM
Pages 448
Release 2008-11-06
Genre Mathematics
ISBN 0898716594

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This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.

Modern Computational Finance

Modern Computational Finance
Title Modern Computational Finance PDF eBook
Author Antoine Savine
Publisher John Wiley & Sons
Pages 592
Release 2018-11-20
Genre Mathematics
ISBN 1119539455

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Arguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities, within seconds, on light hardware. AAD recently became a centerpiece of modern financial systems and a key skill for all quantitative analysts, developers, risk professionals or anyone involved with derivatives. It is increasingly taught in Masters and PhD programs in finance. Danske Bank's wide scale implementation of AAD in its production and regulatory systems won the In-House System of the Year 2015 Risk award. The Modern Computational Finance books, written by three of the very people who designed Danske Bank's systems, offer a unique insight into the modern implementation of financial models. The volumes combine financial modelling, mathematics and programming to resolve real life financial problems and produce effective derivatives software. This volume is a complete, self-contained learning reference for AAD, and its application in finance. AAD is explained in deep detail throughout chapters that gently lead readers from the theoretical foundations to the most delicate areas of an efficient implementation, such as memory management, parallel implementation and acceleration with expression templates. The book comes with professional source code in C++, including an efficient, up to date implementation of AAD and a generic parallel simulation library. Modern C++, high performance parallel programming and interfacing C++ with Excel are also covered. The book builds the code step-by-step, while the code illustrates the concepts and notions developed in the book.

Automatic Differentiation: Applications, Theory, and Implementations

Automatic Differentiation: Applications, Theory, and Implementations
Title Automatic Differentiation: Applications, Theory, and Implementations PDF eBook
Author H. Martin Bücker
Publisher Springer Science & Business Media
Pages 370
Release 2006-02-03
Genre Computers
ISBN 3540284389

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Covers the state of the art in automatic differentiation theory and practice. Intended for computational scientists and engineers, this book aims to provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.