Author : Arnold R. Krommer
Publisher : SIAM
Page : 449 pages
File Size : 29,2 MB
Release : 1998-01-01
Category : Mathematics
ISBN : 0898713749
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.
Author : Ernst Hairer
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 13,8 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662050188
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.
Author : Prem K. Kythe
Publisher : CRC Press
Page : 622 pages
File Size : 22,48 MB
Release : 2004-12-20
Category : Mathematics
ISBN : 1135437521
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.
Author : Ron Sun
Publisher : Springer
Page : 490 pages
File Size : 29,51 MB
Release : 2007-08-19
Category : Computers
ISBN : 0585295999
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.
Author : Manuel Bronstein
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 11,79 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 3662033860
This first volume in the series "Algorithms and Computation in Mathematics", is destined to become the standard reference work in the field. Manuel Bronstein is the number-one expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.
Author : Hedva Spitzer
Publisher : Frontiers Media SA
Page : 233 pages
File Size : 48,47 MB
Release : 2020-05-26
Category :
ISBN : 2889635104
Author : Julia Trommershauser
Publisher : Oxford University Press
Page : 461 pages
File Size : 26,54 MB
Release : 2011-09-21
Category : Psychology
ISBN : 019987476X
This book is concerned with sensory cue integration both within and between sensory modalities, and focuses on the emerging way of thinking about cue combination in terms of uncertainty. These probabilistic approaches derive from the realization that our sensors are noisy and moreover are often affected by ambiguity. For example, mechanoreceptor outputs are variable and they cannot distinguish if a perceived force is caused by the weight of an object or by force we are producing ourselves. The probabilistic approaches elaborated in this book aim at formalizing the uncertainty of cues. They describe cue combination as the nervous system's attempt to minimize uncertainty in its estimates and to choose successful actions. Some computational approaches described in the chapters of this book are concerned with the application of such statistical ideas to real-world cue-combination problems. Others ask how uncertainty may be represented in the nervous system and used for cue combination. Importantly, across behavioral, electrophysiological and theoretical approaches, Bayesian statistics is emerging as a common language in which cue-combination problems can be expressed.
Author : Aman Yadav
Publisher : Routledge
Page : 218 pages
File Size : 30,51 MB
Release : 2021-11-22
Category : Education
ISBN : 1000452638
Computational Thinking in Education explores the relevance of computational thinking in primary and secondary education. As today’s school-aged students prepare to live and work in a thoroughly digitized world, computer science is providing a wealth of new learning concepts and opportunities across domains. This book offers a comprehensive overview of computational thinking, its history, implications for equity and inclusion, analyses of competencies in practice, and integration into learning, instruction, and assessment through scaffolded teacher education. Computer science education faculty and pre- and in-service educators will find a fresh pedagogical approach to computational thinking in primary and secondary classrooms.
Author : R. Piessens
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 44,92 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642617867
1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as orthogo nal polynomials, Fourier series and number theory have had important implications for the evaluation of integrals. We denote the problem addressed here as numerical integration or numerical quadrature. Over the years analysts and engineers have contributed to a growing body of theorems, algorithms and lately, programs, for the solution of this specific problem. Much effort has been devoted to techniques for the analytic evalua tion of integrals. However, most routine integrals in practical scien tific work are incapable of being evaluated in closed form. Even if an expression can be derived for the value of an integral, often this reveals itself only after inordinate amounts of error prone algebraic manipulation. Recently some computer procedures have been developed which can perform analytic integration when it is possible.
Author : Eugene Fiume
Publisher : CRC Press
Page : 322 pages
File Size : 45,76 MB
Release : 2018-10-08
Category : Mathematics
ISBN : 1439864462
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.
