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Author: R. T. Gregory
Publisher: Springer Science & Business Media
ISBN: 1461252423
Category : Mathematics
Languages : en
Pages : 204
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Book Description
This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.
Author: R. T. Gregory
Publisher: Springer Science & Business Media
ISBN: 1461252423
Category : Mathematics
Languages : en
Pages : 204
Get Book Here
Book Description
This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.
Author: C. Brezinski
Publisher: Elsevier
ISBN: 0444598588
Category : Mathematics
Languages : en
Pages : 512
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Book Description
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.
Author: Peter M.A. Sloot
Publisher: Springer
ISBN: 3540460438
Category : Computers
Languages : en
Pages : 1132
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Book Description
Computational Science is the scienti?c discipline that aims at the development and understanding of new computational methods and techniques to model and simulate complex systems. The area of application includes natural systems – such as biology, envir- mental and geo-sciences, physics, and chemistry – and synthetic systems such as electronics and ?nancial and economic systems. The discipline is a bridge b- ween ‘classical’ computer science – logic, complexity, architecture, algorithms – mathematics, and the use of computers in the aforementioned areas. The relevance for society stems from the numerous challenges that exist in the various science and engineering disciplines, which can be tackled by advances made in this ?eld. For instance new models and methods to study environmental issues like the quality of air, water, and soil, and weather and climate predictions through simulations, as well as the simulation-supported development of cars, airplanes, and medical and transport systems etc. Paraphrasing R. Kenway (R.D. Kenway, Contemporary Physics. 1994): ‘There is an important message to scientists, politicians, and industrialists: in the future science, the best industrial design and manufacture, the greatest medical progress, and the most accurate environmental monitoring and forecasting will be done by countries that most rapidly exploit the full potential ofcomputational science’. Nowadays we have access to high-end computer architectures and a large range of computing environments, mainly as a consequence of the enormous s- mulus from the various international programs on advanced computing, e.g.
Author: Victor Greiff
Publisher: Frontiers Media SA
ISBN: 2889633888
Category :
Languages : en
Pages : 358
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Book Description
Author: J. C. Misra
Publisher: Alpha Science Int'l Ltd.
ISBN: 9788173194900
Category : Computers
Languages : en
Pages : 540
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Book Description
This comprehensive volume introduces educational units dealing with important topics in Mathematics, Modelling and Algorithms. Key Features: Illustrative examples and exercises Comprehensive bibliography
Author: Vladimir P. Gerdt
Publisher: Springer Science & Business Media
ISBN: 3642152732
Category : Computers
Languages : en
Pages : 314
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Book Description
This book constitutes the refereed proceedings of the 12th International Workshop on Computer Algebra in Scientific Computing, CASC 2010, held in Tsakhadzor, Armenia, in September 2010. The book includes two invited talks and an abstract in addition to 23 full papers.
Author: Suresh Chandra Satapathy
Publisher: Springer Nature
ISBN: 9811615020
Category : Technology & Engineering
Languages : en
Pages : 801
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Book Description
This book presents best selected papers presented at the 4th International Conference on Smart Computing and Informatics (SCI 2020), held at the Department of Computer Science and Engineering, Vasavi College of Engineering (Autonomous), Hyderabad, Telangana, India. It presents advanced and multi-disciplinary research towards the design of smart computing and informatics. The theme is on a broader front which focuses on various innovation paradigms in system knowledge, intelligence and sustainability that may be applied to provide realistic solutions to varied problems in society, environment and industries. The scope is also extended towards the deployment of emerging computational and knowledge transfer approaches, optimizing solutions in various disciplines of science, technology and health care.
Author: Robert L May
Publisher: World Scientific
ISBN: 981454728X
Category :
Languages : en
Pages : 902
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Book Description
This proceedings contains seven invited papers and 100 contributed papers. The topics covered range from studies of theoretical aspects of computational methods through to simulations of large-scale industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Developers and users of computational techniques who wish to keep up with recent developments in the application of modern computational technology to problems in science and engineering will find much of interest in this volume.
Author: Justin Solomon
Publisher: CRC Press
ISBN: 1482251892
Category : Computers
Languages : en
Pages : 400
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Book Description
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Author: Osvaldo Gervasi
Publisher: Springer Nature
ISBN: 3031371089
Category : Computers
Languages : en
Pages : 779
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Book Description
This nine-volume set LNCS 14104 – 14112 constitutes the refereed workshop proceedings of the 23rd International Conference on Computational Science and Its Applications, ICCSA 2023, held at Athens, Greece, during July 3–6, 2023. The 350 full papers and 29 short papers and 2 PHD showcase papers included in this volume were carefully reviewed and selected from a total of 876 submissions. These nine-volumes includes the proceedings of the following workshops: Advances in Artificial Intelligence Learning Technologies: Blended Learning, STEM, Computational Thinking and Coding (AAILT 2023); Advanced Processes of Mathematics and Computing Models in Complex Computational Systems (ACMC 2023); Artificial Intelligence supported Medical data examination (AIM 2023); Advanced and Innovative web Apps (AIWA 2023); Assessing Urban Sustainability (ASUS 2023); Advanced Data Science Techniques with applications in Industry and Environmental Sustainability (ATELIERS 2023); Advances in Web Based Learning (AWBL 2023); Blockchain and Distributed Ledgers: Technologies and Applications (BDLTA 2023); Bio and Neuro inspired Computing and Applications (BIONCA 2023); Choices and Actions for Human Scale Cities: Decision Support Systems (CAHSC-DSS 2023); and Computational and Applied Mathematics (CAM 2023).
