Automatic Differentiation In Matlab Using Admat With Applications
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Automatic Differentiation In Matlab Using Admat With Applications
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Author : Thomas F. Coleman
language : en
Publisher: SIAM
Release Date : 2016-06-20
Automatic Differentiation In Matlab Using Admat With Applications written by Thomas F. Coleman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Science categories.
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 Applications discusses 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.
Petsc For Partial Differential Equations Numerical Solutions In C And Python
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Author : Ed Bueler
language : en
Publisher: SIAM
Release Date : 2020-10-22
Petsc For Partial Differential Equations Numerical Solutions In C And Python written by Ed Bueler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.
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.
Automatic Differentiation Applications Theory And Implementations
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Author : H. Martin Bücker
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-03
Automatic Differentiation Applications Theory And Implementations written by H. Martin Bücker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-03 with Computers categories.
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.
A Software Repository For Gaussian Quadratures And Christoffel Functions
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Author : Walter Gautschi
language : en
Publisher: SIAM
Release Date : 2020-10-30
A Software Repository For Gaussian Quadratures And Christoffel Functions written by Walter Gautschi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-30 with Mathematics categories.
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.
A Software Repository For Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: SIAM
Release Date : 2018-03-20
A Software Repository For Orthogonal Polynomials written by Walter Gautschi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-20 with Science categories.
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.????
Bits And Bugs
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Author : Thomas Huckle
language : en
Publisher: SIAM
Release Date : 2019-03-08
Bits And Bugs written by Thomas Huckle and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-08 with Mathematics categories.
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.
Introduction To High Performance Scientific Computing
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Author : David L. Chopp
language : en
Publisher: SIAM
Release Date : 2019-03-01
Introduction To High Performance Scientific Computing written by David L. Chopp and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-01 with Mathematics categories.
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.
Object Oriented Methods For Interoperable Scientific And Engineering Computing
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Author : Michael E. Henderson
language : en
Publisher: SIAM
Release Date : 1999-01-01
Object Oriented Methods For Interoperable Scientific And Engineering Computing written by Michael E. Henderson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Technology & Engineering categories.
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.
Uncertainty Quantification
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Author : Ralph C. Smith
language : en
Publisher: SIAM
Release Date : 2024-09-13
Uncertainty Quantification written by Ralph C. Smith and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-13 with Mathematics categories.
Uncertainty quantification serves a fundamental role when establishing the predictive capabilities of simulation models. This book provides a comprehensive and unified treatment of the mathematical, statistical, and computational theory and methods employed to quantify uncertainties associated with models from a wide range of applications. Expanded and reorganized, the second edition includes advances in the field and provides a comprehensive sensitivity analysis and uncertainty quantification framework for models from science and engineering. It contains new chapters on random field representations, observation models, parameter identifiability and influence, active subspace analysis, and statistical surrogate models, and a completely revised chapter on local sensitivity analysis. Other updates to the second edition are the inclusion of over 100 exercises and many new examples — several of which include data — and UQ Crimes listed throughout the text to identify common misconceptions and guide readers entering the field. Uncertainty Quantification: Theory, Implementation, and Applications, Second Edition is intended for advanced undergraduate and graduate students as well as researchers in mathematics, statistics, engineering, physical and biological sciences, operations research, and computer science. Readers are assumed to have a basic knowledge of probability, linear algebra, differential equations, and introductory numerical analysis. The book can be used as a primary text for a one-semester course on sensitivity analysis and uncertainty quantification or as a supplementary text for courses on surrogate and reduced-order model construction and parameter identifiability analysis.
Computational Science Iccs 2006
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2006
Computational Science Iccs 2006 written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Computational complexity categories.