Computational Integration

Computational Integration
Author: Arnold R. Krommer
Publisher: SIAM
Total Pages: 449
Release: 1998-01-01
Genre: Mathematics
ISBN: 0898713749

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This survey covers a wide range of topics fundamental to calculating integrals on computer systems and discusses both the theoretical and computational aspects of numerical and symbolic methods. It includes extensive sections on one- and multidimensional integration formulas, like polynomial, number-theoretic, and pseudorandom formulas, and deals with issues concerning the construction of numerical integration algorithms.

Handbook of Computational Methods for Integration

Handbook of Computational Methods for Integration
Author: Prem K. Kythe
Publisher: CRC Press
Total Pages: 622
Release: 2004-12-20
Genre: Mathematics
ISBN: 1135437521

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During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-ended. The importance of numerical integration in so many areas of science and technology has made a practical, up-to-date reference on this subject long overdue. The Handbook of Computational Methods for Integration discusses quadrature rules for finite and infinite range integrals and their applications in differential and integral equations, Fourier integrals and transforms, Hartley transforms, fast Fourier and Hartley transforms, Laplace transforms and wavelets. The practical, applied perspective of this book makes it unique among the many theoretical books on numerical integration and quadrature. It will be a welcomed addition to the libraries of applied mathematicians, scientists, and engineers in virtually every discipline.

Geometric Numerical Integration

Geometric Numerical Integration
Author: Ernst Hairer
Publisher: Springer Science & Business Media
Total Pages: 526
Release: 2013-03-09
Genre: Mathematics
ISBN: 3662050188

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This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.

Handbook of Computational Methods for Integration

Handbook of Computational Methods for Integration
Author: Prem K. Kythe
Publisher: CRC Press
Total Pages: 621
Release: 2004-12-20
Genre: Mathematics
ISBN: 0203490304

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During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-

Integrated Computational Materials Engineering

Integrated Computational Materials Engineering
Author: National Research Council
Publisher: National Academies Press
Total Pages: 152
Release: 2008-10-24
Genre: Technology & Engineering
ISBN: 0309119995

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Integrated computational materials engineering (ICME) is an emerging discipline that can accelerate materials development and unify design and manufacturing. Developing ICME is a grand challenge that could provide significant economic benefit. To help develop a strategy for development of this new technology area, DOE and DoD asked the NRC to explore its benefits and promises, including the benefits of a comprehensive ICME capability; to establish a strategy for development and maintenance of an ICME infrastructure, and to make recommendations about how best to meet these opportunities. This book provides a vision for ICME, a review of case studies and lessons learned, an analysis of technological barriers, and an evaluation of ways to overcome cultural and organizational challenges to develop the discipline.

Computational Architectures Integrating Neural and Symbolic Processes

Computational Architectures Integrating Neural and Symbolic Processes
Author: Ron Sun
Publisher: Springer
Total Pages: 490
Release: 2007-08-19
Genre: Computers
ISBN: 0585295999

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Computational Architectures Integrating Neural and Symbolic Processes: A Perspective on the State of the Art focuses on a currently emerging body of research. With the reemergence of neural networks in the 1980s with their emphasis on overcoming some of the limitations of symbolic AI, there is clearly a need to support some form of high-level symbolic processing in connectionist networks. As argued by many researchers, on both the symbolic AI and connectionist sides, many cognitive tasks, e.g. language understanding and common sense reasoning, seem to require high-level symbolic capabilities. How these capabilities are realized in connectionist networks is a difficult question and it constitutes the focus of this book. Computational Architectures Integrating Neural and Symbolic Processes addresses the underlying architectural aspects of the integration of neural and symbolic processes. In order to provide a basis for a deeper understanding of existing divergent approaches and provide insight for further developments in this field, this book presents: (1) an examination of specific architectures (grouped together according to their approaches), their strengths and weaknesses, why they work, and what they predict, and (2) a critique/comparison of these approaches. Computational Architectures Integrating Neural and Symbolic Processes is of interest to researchers, graduate students, and interested laymen, in areas such as cognitive science, artificial intelligence, computer science, cognitive psychology, and neurocomputing, in keeping up-to-date with the newest research trends. It is a comprehensive, in-depth introduction to this new emerging field.

An Introduction to Scientific, Symbolic, and Graphical Computation

An Introduction to Scientific, Symbolic, and Graphical Computation
Author: Eugene Fiume
Publisher: CRC Press
Total Pages: 322
Release: 2018-10-08
Genre: Mathematics
ISBN: 1439864462

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This down-to-earth introduction to computation makes use of the broad array of techniques available in the modern computing environment. A self-contained guide for engineers and other users of computational methods, it has been successfully adopted as a text in teaching the next generation of mathematicians and computer graphics majors.

Proceedings of the 2nd World Congress on Integrated Computational Materials Engineering (ICME)

Proceedings of the 2nd World Congress on Integrated Computational Materials Engineering (ICME)
Author: Mei Li
Publisher: Springer
Total Pages: 303
Release: 2016-12-19
Genre: Technology & Engineering
ISBN: 3319481940

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This book represents a collection of papers presented at the 2nd World Congress on Integrated Computational Materials Engineering (ICME), a specialty conference organized by The Minerals, Metals & Materials Society (TMS).

Computational Methods for Numerical Analysis with R

Computational Methods for Numerical Analysis with R
Author: James P Howard, II
Publisher: CRC Press
Total Pages: 257
Release: 2017-07-12
Genre: Mathematics
ISBN: 1498723640

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Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.