Automatic Differentiation Of Algorithms

Author : George Corliss,Christele Faure,Andreas Griewank,Laurent Hascoet,Uwe Naumann
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 41,7 Mb
Release : 2013-11-21
Category : Computers
ISBN : 9781461300755

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Automatic Differentiation of Algorithms by George Corliss,Christele Faure,Andreas Griewank,Laurent Hascoet,Uwe Naumann Pdf

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.

Author : Andreas Griewank
Publisher : Society for Industrial & Applied
Page : 353 pages
File Size : 49,9 Mb
Release : 1991
Category : Computers
ISBN : 089871284X

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Automatic Differentiation of Algorithms by Andreas Griewank Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Christian H. Bischof,H. Martin Bücker,Paul Hovland,Uwe Naumann,Jean Utke
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 50,7 Mb
Release : 2008-08-17
Category : Computers
ISBN : 9783540689423

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Advances in Automatic Differentiation by Christian H. Bischof,H. Martin Bücker,Paul Hovland,Uwe Naumann,Jean Utke Pdf

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.

Author : Andreas Griewank,Andrea Walther
Publisher : SIAM
Page : 448 pages
File Size : 55,6 Mb
Release : 2008-11-06
Category : Mathematics
ISBN : 9780898716597

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Evaluating Derivatives by Andreas Griewank,Andrea Walther Pdf

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.

Author : Andreas Griewank,Andrea Walther
Publisher : SIAM
Page : 438 pages
File Size : 48,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898717761

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Evaluating Derivatives by Andreas Griewank,Andrea Walther Pdf

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.

Author : Shaun Forth,Paul Hovland,Eric Phipps,Jean Utke,Andrea Walther
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 42,6 Mb
Release : 2012-07-30
Category : Mathematics
ISBN : 9783642300233

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Recent Advances in Algorithmic Differentiation by Shaun Forth,Paul Hovland,Eric Phipps,Jean Utke,Andrea Walther Pdf

The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the efficiency of matrix-operation derivatives, detection and exploitation of sparsity, partial separability, the treatment of nonsmooth functions, and other high-level mathematical aspects of the numerical computations to be differentiated. Applications stem from the Earth sciences, nuclear engineering, fluid dynamics, and chemistry, to name just a few. In many cases the applications in a given area of science or engineering share characteristics that require specific approaches to enable AD capabilities or provide an opportunity for efficiency gains in the derivative computation. The description of these characteristics and of the techniques for successfully using AD should make the proceedings a valuable source of information for users of AD tools.

Author : Uwe Naumann
Publisher : SIAM
Page : 358 pages
File Size : 47,5 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 1611972078

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The Art of Differentiating Computer Programs by Uwe Naumann Pdf

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.

Author : Martin Bücker
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 43,8 Mb
Release : 2006-01-23
Category : Computers
ISBN : 3540284036

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Automatic Differentiation: Applications, Theory, and Implementations by Martin Bücker Pdf

This collection covers the state of the art in automatic differentiation theory and practice. Practitioners and students will learn about advances in automatic differentiation techniques and strategies for the implementation of robust and powerful tools. Computational scientists and engineers will benefit from the discussion of applications, which provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.

Author : Louis B. Rall
Publisher : Springer
Page : 194 pages
File Size : 47,5 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015000972409

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Automatic Differentiation by Louis B. Rall Pdf

Author : Andreas Griewank
Publisher : Society for Industrial and Applied Mathematics
Page : 390 pages
File Size : 50,9 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 0898714516

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Evaluating Derivatives by Andreas Griewank Pdf

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.

Author : Marc Henrard
Publisher : Springer
Page : 103 pages
File Size : 46,8 Mb
Release : 2017-09-04
Category : Business & Economics
ISBN : 9783319539799

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Algorithmic Differentiation in Finance Explained by Marc Henrard Pdf

This book provides the first practical guide to the function and implementation of algorithmic differentiation in finance. Written in a highly accessible way, Algorithmic Differentiation Explained will take readers through all the major applications of AD in the derivatives setting with a focus on implementation. Algorithmic Differentiation (AD) has been popular in engineering and computer science, in areas such as fluid dynamics and data assimilation for many years. Over the last decade, it has been increasingly (and successfully) applied to financial risk management, where it provides an efficient way to obtain financial instrument price derivatives with respect to the data inputs. Calculating derivatives exposure across a portfolio is no simple task. It requires many complex calculations and a large amount of computer power, which in prohibitively expensive and can be time consuming. Algorithmic differentiation techniques can be very successfully in computing Greeks and sensitivities of a portfolio with machine precision. Written by a leading practitioner who works and programmes AD, it offers a practical analysis of all the major applications of AD in the derivatives setting and guides the reader towards implementation. Open source code of the examples is provided with the book, with which readers can experiment and perform their own test scenarios without writing the related code themselves.

Author : M. Berz
Publisher : Soc for Industrial & Applied Math
Page : 458 pages
File Size : 47,5 Mb
Release : 1996
Category : Computers
ISBN : UOM:39015049289773

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Computational Differentiation by M. Berz Pdf

This volume encompasses both the automatic transformation of computer programs as well as the methodologies for the efficient exploitation of mathematical underpinnings or program structure.

Author : Roy Featherstone
Publisher : Springer
Page : 276 pages
File Size : 41,7 Mb
Release : 2014-11-10
Category : Education
ISBN : 9781489975607

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Rigid Body Dynamics Algorithms by Roy Featherstone Pdf

Rigid Body Dynamics Algorithms presents the subject of computational rigid-body dynamics through the medium of spatial 6D vector notation. It explains how to model a rigid-body system and how to analyze it, and it presents the most comprehensive collection of the best rigid-body dynamics algorithms to be found in a single source. The use of spatial vector notation greatly reduces the volume of algebra which allows systems to be described using fewer equations and fewer quantities. It also allows problems to be solved in fewer steps, and solutions to be expressed more succinctly. In addition algorithms are explained simply and clearly, and are expressed in a compact form. The use of spatial vector notation facilitates the implementation of dynamics algorithms on a computer: shorter, simpler code that is easier to write, understand and debug, with no loss of efficiency.

Author : L. B. Rall
Publisher : Unknown
Page : 180 pages
File Size : 43,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662178680

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Automatic Differentiation by L. B. Rall Pdf

Author : Mykel J. Kochenderfer,Tim A. Wheeler
Publisher : MIT Press
Page : 521 pages
File Size : 40,7 Mb
Release : 2019-03-12
Category : Computers
ISBN : 9780262039420

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Algorithms for Optimization by Mykel J. Kochenderfer,Tim A. Wheeler Pdf

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.