Automatic Differentiation In Matlab Using Admat With Applications

Author : Thomas F. Coleman,Wei Xu
Publisher : SIAM
Page : 105 pages
File Size : 47,5 Mb
Release : 2016-06-20
Category : Science
ISBN : 9781611974362

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Automatic Differentiation in MATLAB Using ADMAT with Applications by Thomas F. Coleman,Wei Xu Pdf

The calculation of partial derivatives is a fundamental need in scientific computing. Automatic differentiation (AD) can be applied straightforwardly to obtain all necessary partial derivatives (usually first and, possibly, second derivatives) regardless of a code?s complexity. However, the space and time efficiency of AD can be dramatically improved?sometimes transforming a problem from intractable to highly feasible?if inherent problem structure is used to apply AD in a judicious manner. Automatic Differentiation in MATLAB using ADMAT with Applicationsödiscusses the efficient use of AD to solve real problems, especially multidimensional zero-finding and optimization, in the MATLAB environment. This book is concerned with the determination of the first and second derivatives in the context of solving scientific computing problems with an emphasis on optimization and solutions to nonlinear systems. The authors focus on the application rather than the implementation of AD, solve real nonlinear problems with high performance by exploiting the problem structure in the application of AD, and provide many easy to understand applications, examples, and MATLAB templates.ö

Author : H. Martin Bücker,George Corliss,Paul Hovland,Uwe Naumann,Boyana Norris
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 47,6 Mb
Release : 2006-02-03
Category : Computers
ISBN : 9783540284383

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Automatic Differentiation: Applications, Theory, and Implementations by H. Martin Bücker,George Corliss,Paul Hovland,Uwe Naumann,Boyana Norris Pdf

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.

Author : Ed Bueler
Publisher : SIAM
Page : 407 pages
File Size : 43,9 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781611976311

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PETSc for Partial Differential Equations: Numerical Solutions in C and Python by Ed Bueler Pdf

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Author : Walter Gautschi
Publisher : SIAM
Page : 152 pages
File Size : 49,9 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9781611976359

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A Software Repository for Gaussian Quadratures and Christoffel Functions by Walter Gautschi Pdf

This companion piece to the author’s 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions. The repository contains 60+ datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials. Scientists, engineers, applied mathematicians, and statisticians will find the book of interest.

Author : Sivan Toledo
Publisher : SIAM
Page : 216 pages
File Size : 43,7 Mb
Release : 2020-09-17
Category : Technology & Engineering
ISBN : 9781611976298

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Location Estimation from the Ground Up by Sivan Toledo Pdf

The location of an object can often be determined from indirect measurements using a process called estimation. This book explains the mathematical formulation of location-estimation problems and the statistical properties of these mathematical models. It also presents algorithms that are used to resolve these models to obtain location estimates, including the simplest linear models, nonlinear models (location estimation using satellite navigation systems and estimation of the signal arrival time from those satellites), dynamical systems (estimation of an entire path taken by a vehicle), and models with integer ambiguities (GPS location estimation that is centimeter-level accurate). Location Estimation from the Ground Up clearly presents analytic and algorithmic topics not covered in other books, including simple algorithms for Kalman filtering and smoothing, the solution of separable nonlinear optimization problems, estimation with integer ambiguities, and the implicit-function approach to estimating covariance matrices when the estimator is a minimizer or maximizer. It takes a unified approach to estimation while highlighting the differences between classes of estimation problems. The only book on estimation written for math and computer science students and graduates, it includes problems at the end of each chapter, many with solutions, to help readers deepen their understanding of the material and guide them through small programming projects that apply theory and algorithms to the solution of real-world location-estimation problems. The book’s core audience consists of engineers, including software engineers and algorithm developers, and graduate students who work on location-estimation projects and who need help translating the theory into algorithms, code, and deep understanding of the problem in front of them. Instructors in mathematics, computer science, and engineering may also find the book of interest as a primary or supplementary text for courses in location estimation and navigation.

Author : David L. Chopp
Publisher : SIAM
Page : 470 pages
File Size : 42,9 Mb
Release : 2019-03-01
Category : Mathematics
ISBN : 9781611975635

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Introduction to High Performance Scientific Computing by David L. Chopp Pdf

Based on a course developed by the author, Introduction to High Performance Scientific Computing introduces methods for adding parallelism to numerical methods for solving differential equations. It contains exercises and programming projects that facilitate learning as well as examples and discussions based on the C programming language, with additional comments for those already familiar with C++. The text provides an overview of concepts and algorithmic techniques for modern scientific computing and is divided into six self-contained parts that can be assembled in any order to create an introductory course using available computer hardware. Part I introduces the C programming language for those not already familiar with programming in a compiled language. Part II describes parallelism on shared memory architectures using OpenMP. Part III details parallelism on computer clusters using MPI for coordinating a computation. Part IV demonstrates the use of graphical programming units (GPUs) to solve problems using the CUDA language for NVIDIA graphics cards. Part V addresses programming on GPUs for non-NVIDIA graphics cards using the OpenCL framework. Finally, Part VI contains a brief discussion of numerical methods and applications, giving the reader an opportunity to test the methods on typical computing problems.

Author : Thomas Huckle,Tobias Neckel
Publisher : SIAM
Page : 251 pages
File Size : 51,6 Mb
Release : 2019-03-08
Category : Mathematics
ISBN : 9781611975567

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Bits and Bugs by Thomas Huckle,Tobias Neckel Pdf

In scientific computing (also known as computational science), advanced computing capabilities are used to solve complex problems. This self-contained book describes and analyzes reported software failures related to the major topics within scientific computing: mathematical modeling of phenomena; numerical analysis (number representation, rounding, conditioning); mathematical aspects and complexity of algorithms, systems, or software; concurrent computing (parallelization, scheduling, synchronization); and numerical data (such as input of data and design of control logic). Readers will find lists of related, interesting bugs, MATLAB examples, and “excursions” that provide necessary background, as well as an in-depth analysis of various aspects of the selected bugs. Illustrative examples of numerical principles such as machine numbers, rounding errors, condition numbers, and complexity are also included.

Author : Walter Gautschi
Publisher : SIAM
Page : 60 pages
File Size : 45,8 Mb
Release : 2018
Category : Science
ISBN : 9781611975222

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A Software Repository for Orthogonal Polynomials by Walter Gautschi Pdf

A Software Repository for Orthogonal Polynomials is the first book that provides graphs and references to online datasets that enable the generation of a large number of orthogonal polynomials with classical, quasi-classical, and nonclassical weight functions. Useful numerical tables are also included. The book will be of interest to scientists, engineers, applied mathematicians, and statisticians.

Author : Michael E. Henderson,Christopher Radcliff Anderson,Stephen L. Lyons
Publisher : SIAM
Page : 340 pages
File Size : 44,9 Mb
Release : 1999-01-01
Category : Technology & Engineering
ISBN : 0898714451

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Object Oriented Methods for Interoperable Scientific and Engineering Computing by Michael E. Henderson,Christopher Radcliff Anderson,Stephen L. Lyons Pdf

Contains papers presented at the October 1998 SIAM Workshop on Object Oriented Methods for Interoperable Scientific and Engineering Computing that covered a variety of topics and issues related to designing and implementing computational tools for science and engineering.

Author : Vassil N. Alexandrov,G. Dick van Albada,Peter M.A. Sloot,J. J. Dongarra
Publisher : Springer
Page : 1096 pages
File Size : 53,6 Mb
Release : 2006-05-10
Category : Computers
ISBN : 9783540343868

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Computational Science - ICCS 2006 by Vassil N. Alexandrov,G. Dick van Albada,Peter M.A. Sloot,J. J. Dongarra Pdf

This is Volume IV of the four-volume set LNCS 3991-3994 constituting the refereed proceedings of the 6th International Conference on Computational Science, ICCS 2006. The 98 revised full papers and 29 revised poster papers of the main track presented together with 500 accepted workshop papers were carefully reviewed and selected for inclusion in the four volumes. The coverage spans the whole range of computational science.

Author : Anonim
Publisher : Springer Science & Business Media
Page : 1128 pages
File Size : 43,7 Mb
Release : 2006
Category : Computational complexity
ISBN : 9783540343851

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Computational Science - ICCS 2006 by Anonim Pdf

Author : Christian H. Bischof,H. Martin Bücker,Paul Hovland,Uwe Naumann,Jean Utke
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 51,7 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 : Seon Ki Park,Milija Zupanski
Publisher : Cambridge University Press
Page : 413 pages
File Size : 51,5 Mb
Release : 2022-09-29
Category : Science
ISBN : 9781108923897

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Principles of Data Assimilation by Seon Ki Park,Milija Zupanski Pdf

Data assimilation is theoretically founded on probability, statistics, control theory, information theory, linear algebra, and functional analysis. At the same time, data assimilation is a very practical subject, given its goal of estimating the posterior probability density function in realistic high-dimensional applications. This puts data assimilation at the intersection between the contrasting requirements of theory and practice. Based on over twenty years of teaching courses in data assimilation, Principles of Data Assimilation introduces a unique perspective that is firmly based on mathematical theories, but also acknowledges practical limitations of the theory. With the inclusion of numerous examples and practical case studies throughout, this new perspective will help students and researchers to competently interpret data assimilation results and to identify critical challenges of developing data assimilation algorithms. The benefit of information theory also introduces new pathways for further development, understanding, and improvement of data assimilation methods.

Author : Shaun Forth,Paul Hovland,Eric Phipps,Jean Utke,Andrea Walther
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 44,7 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 : L.B. Rall
Publisher : Springer
Page : 166 pages
File Size : 42,5 Mb
Release : 1981-08-01
Category : Mathematics
ISBN : 3540108610

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Automatic Differentiation by L.B. Rall Pdf