Computational Error And Complexity In Science And Engineering

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Computational Error and Complexity in Science and Engineering

Author : Vangipuram Lakshmikantham
Publisher : Elsevier
ISBN 13 : 008045951X
Total Pages : 260 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Computational Error and Complexity in Science and Engineering by : Vangipuram Lakshmikantham

Download or read book Computational Error and Complexity in Science and Engineering written by Vangipuram Lakshmikantham and published by Elsevier. This book was released on 2005-03-04 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book “Computational Error and Complexity in Science and Engineering pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions. Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering. Key Features: - Describes precisely ready-to-use computational error and complexity - Includes simple easy-to-grasp examples wherever necessary. - Presents error and complexity in error-free, parallel, and probabilistic methods. - Discusses deterministic and probabilistic methods with error and complexity. - Points out the scope and limitation of mathematical error-bounds. - Provides a comprehensive up-to-date bibliography after each chapter. · Describes precisely ready-to-use computational error and complexity · Includes simple easy-to-grasp examples wherever necessary. · Presents error and complexity in error-free, parallel, and probabilistic methods. · Discusses deterministic and probabilistic methods with error and complexity. · Points out the scope and limitation of mathematical error-bounds. · Provides a comprehensive up-to-date bibliography after each chapter.

Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers

Author : Moysey Brio
Publisher : Academic Press
ISBN 13 : 9780080917047
Total Pages : 312 pages
Book Rating : 4.9/5 (17 download)

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Book Synopsis Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers by : Moysey Brio

Download or read book Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers written by Moysey Brio and published by Academic Press. This book was released on 2010-09-21 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations

Decision Making in Social Sciences: Between Traditions and Innovations

Author : Daniel Flaut
Publisher : Springer Nature
ISBN 13 : 3030306593
Total Pages : 535 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Decision Making in Social Sciences: Between Traditions and Innovations by : Daniel Flaut

Download or read book Decision Making in Social Sciences: Between Traditions and Innovations written by Daniel Flaut and published by Springer Nature. This book was released on 2019-11-28 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores several branches of the social sciences and their perspectives regarding their relations with decision-making processes: computer science, education, linguistics, sociology, and management. The decision-making process in social contexts is based on the analysis of sound alternatives using evaluative criteria. Therefore, this process is one that can be rational or irrational, and can be based on knowledge and/or beliefs. A decision-making process always produces a final decision, which may or may not imply prompt action, and increases the chances of choosing the best possible alternative. The book is divided into four main parts. The concepts covered in the first part, on computer science, explore how the rise of algorithms and the growth in computing power over the years can influence decision-making processes. In the second part, some traditional and innovative ideas and methods used in education are presented: compulsory schooling, inclusive schools, higher education, etc. In turn, the third part focuses on linguistics aspects, and examines how progress is manifested in language. The fourth part, on sociology, explores how society can be influenced by social norms, human interactions, culture, and religion. Management, regarded as a science of the decision-making process, is explored in the last part of this book. Selected organizations’ strategies, objectives and resources are presented, e.g., human resources, financial resources, and technological resources. The book gathers and presents, in a concise format, a broad range of aspects regarding the decision-making process in social contexts, making it a valuable and unique resource for the scientific community.

Algorithms as a Basis of Modern Applied Mathematics

Author : Šárka Hošková-Mayerová
Publisher : Springer Nature
ISBN 13 : 3030613348
Total Pages : 515 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Algorithms as a Basis of Modern Applied Mathematics by : Šárka Hošková-Mayerová

Download or read book Algorithms as a Basis of Modern Applied Mathematics written by Šárka Hošková-Mayerová and published by Springer Nature. This book was released on 2021-01-13 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a self-contained guide to advanced algorithms and their applications in various fields of science. Gathering contributions by authoritative researchers in the field of mathematics, statistics and computer science, it aims at offering a comprehensive and up-to-date view of algorithms, including the theory behind them, as well as practical considerations, current limitations and solutions. It covers applications in energy management, decision making, computer networks, materials science, mechanics and process optimization. It offers an integrated and timely guide to important algorithms, and represents a valuable reference resource for graduate students and researchers in various fields of applied mathematics, statistics and engineering.

Computational Mathematics, Modelling and Algorithms

Author : J. C. Misra
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9788173194900
Total Pages : 540 pages
Book Rating : 4.1/5 (949 download)

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Book Synopsis Computational Mathematics, Modelling and Algorithms by : J. C. Misra

Download or read book Computational Mathematics, Modelling and Algorithms written by J. C. Misra and published by Alpha Science Int'l Ltd.. This book was released on 2003 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume introduces educational units dealing with important topics in Mathematics, Modelling and Algorithms. Key Features: Illustrative examples and exercises Comprehensive bibliography

Stochastic Modelling in Process Technology

Author : Herold G. Dehling
Publisher : Elsevier
ISBN 13 : 9780080548975
Total Pages : 290 pages
Book Rating : 4.5/5 (489 download)

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Book Synopsis Stochastic Modelling in Process Technology by : Herold G. Dehling

Download or read book Stochastic Modelling in Process Technology written by Herold G. Dehling and published by Elsevier. This book was released on 2007-07-03 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry. This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling. The technique is based on computing the probability distribution for a single particle's position in the process vessel, and/or the particle's properties, as a function of time, rather than - as is traditionally done - basing the model on the formulation and solution of differential conservation equations. Using this technique can greatly simplify the formulation of a model, and even make modelling possible for processes so complex that the traditional method is impracticable. Stochastic modelling has sporadically been used in various branches of process technology under various names and guises. This book gives, as the first, an overview of this work, and shows how these techniques are similar in nature, and make use of the same basic mathematical tools and techniques. The book also demonstrates how stochastic modelling may be implemented by describing example cases, and shows how a stochastic model may be formulated for a case, which cannot be described by formulating and solving differential balance equations. Introduction to stochastic process modelling as an alternative modelling technique Shows how stochastic modelling may be succesful where the traditional technique fails Overview of stochastic modelling in process technology in the research literature Illustration of the principle by a wide range of practical examples In-depth and self-contained discussions Points the way to both mathematical and technological research in a new, rewarding field

Advances in Computer Science and Information Technology. Computer Science and Engineering

Author : Natarajan Meghanathan
Publisher : Springer
ISBN 13 : 3642273084
Total Pages : 667 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Advances in Computer Science and Information Technology. Computer Science and Engineering by : Natarajan Meghanathan

Download or read book Advances in Computer Science and Information Technology. Computer Science and Engineering written by Natarajan Meghanathan and published by Springer. This book was released on 2012-04-24 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume set LNICST 84 - LNICST 86 constitute the refereed proceedings ofthe Second International Conference on Computer Science and InformationTechnology, CCSIT 2012, held in Bangalore, India, in January 2012. The 70 revised full papers presented in this volume were carefullyreviewed and selected from numerous submissions and address all major fields ofthe Computer Science and Information Technology in theoretical, methodological,and practical or applicative aspects. The papers feature cutting-edge developmentand current research in computer science and engineering.

Bits and Bugs

Author : Thomas Huckle
Publisher : SIAM
ISBN 13 : 1611975557
Total Pages : 264 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Bits and Bugs by : Thomas Huckle

Download or read book Bits and Bugs written by Thomas Huckle and published by SIAM. This book was released on 2019-03-08 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. ?

Computational Science and Engineering

Author : Rayner Alfred
Publisher : Trans Tech Publications Ltd
ISBN 13 : 3035734011
Total Pages : 310 pages
Book Rating : 4.0/5 (357 download)

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Book Synopsis Computational Science and Engineering by : Rayner Alfred

Download or read book Computational Science and Engineering written by Rayner Alfred and published by Trans Tech Publications Ltd. This book was released on 2019-06-10 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3rd International Conference on Computational Science and Engineering (ICCSE 2018) Selected, peer reviewed papers from the Third International Conference on Computational Science and Engineering (ICCSE2018), August 29-30, 2018, Kota Kinabalu, Sabah, Malaysia

Scientific Computing

Author : Michael T. Heath
Publisher : SIAM
ISBN 13 : 1611975573
Total Pages : 567 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Scientific Computing by : Michael T. Heath

Download or read book Scientific Computing written by Michael T. Heath and published by SIAM. This book was released on 2018-11-14 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

Insight Through Computing

Author : Charles F. Van Loan
Publisher : SIAM
ISBN 13 : 0898717647
Total Pages : 437 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Insight Through Computing by : Charles F. Van Loan

Download or read book Insight Through Computing written by Charles F. Van Loan and published by SIAM. This book was released on 2010-01-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to computer-based problem-solving using the MATLAB environment is highly recommended for students wishing to learn the concepts and develop the programming skills that are fundamental to computational science and engineering (CSE). Through a 'teaching by examples' approach, the authors pose strategically chosen problems to help first-time programmers learn these necessary concepts and skills. Each section formulates a problem and then introduces those new MATLAB language features that are necessary to solve it. This approach puts problem-solving and algorithmic thinking first and syntactical details second. Each solution is followed by a 'talking point' that concerns some related, larger issue associated with CSE. Collectively, the worked examples, talking points, and 300+ homework problems build intuition for the process of discretization and an appreciation for dimension, inexactitude, visualization, randomness, and complexity. This sets the stage for further coursework in CSE areas.

Zero

Author : Syamal K. Sen
Publisher : Academic Press
ISBN 13 : 0128046244
Total Pages : 166 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Zero by : Syamal K. Sen

Download or read book Zero written by Syamal K. Sen and published by Academic Press. This book was released on 2015-11-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zero indicates the absence of a quantity or a magnitude. It is so deeply rooted in our psyche today that nobody will possibly ask "What is zero?" From the beginning of the very creation of life, the feeling of lack of something or the vision of emptiness/void has been embedded by the creator in all living beings. While recognizing different things as well as the absence of one of these things are easy, it is not so easy to fathom the complete nothingness viz. the universal void. Although we have a very good understanding of nothingness or, equivalently, a zero today, our forefathers had devoted countless hours and arrived at the representation and integration of zero and its compatibility not only with all non-zero numbers but also with all conceivable environments only after many painstaking centuries. Zero can be viewed/perceived in two distinct forms: (i) as a number in our mundane affairs and (ii) as the horrific void or Absolute Reality in the spiritual plane/the ultimate state of mind. Presented are the reasons why zero is a landmark discovery and why it has the potential to conjure up in an intense thinker the dreadful nothingness unlike those of other numbers such as 1, 2, and 3. Described are the representation of zero and its history including its deeper understanding via calculus, its occurrences and various roles in different countries as well as in sciences/engineering along with a stress on the Indian zero that is accepted as the time-invariant unique absolute zero. This is followed by the significant distinction between mathematics and computational mathematics and the concerned differences between the unique absolute zero and non-unique relative numerical zeros and their impact and importance in computations on a digital computer. Introduces the history of the value of zero and why it was a landmark discovery Discusses how zero is used in science and engineering and its use in different countries Explains how zero affects different mathematics and calculus

Theory of Computational Complexity

Author : Ding-Zhu Du
Publisher : John Wiley & Sons
ISBN 13 : 1118306082
Total Pages : 517 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis Theory of Computational Complexity by : Ding-Zhu Du

Download or read book Theory of Computational Complexity written by Ding-Zhu Du and published by John Wiley & Sons. This book was released on 2014-06-30 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "... complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity." —Zentralblatt MATH A thorough revision based on advances in the field of computational complexity and readers’ feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered. Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent developments on areas such as NP-completeness theory, as well as: A new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science Additional exercises at varying levels of difficulty to further test comprehension of the presented material End-of-chapter literature reviews that summarize each topic and offer additional sources for further study Theory of Computational Complexity, Second Edition, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.

Information-based Complexity

Author : Joseph Frederick Traub
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Information-based Complexity by : Joseph Frederick Traub

Download or read book Information-based Complexity written by Joseph Frederick Traub and published by . This book was released on 1988 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive treatment of information-based complexity, the branch of computational complexity that deals with the intrinsic difficulty of the approximate solution of problems for which the information is partial, noisy, and priced. Such problems arise in many areas including economics, physics, human and robotic vision, scientific and engineering computation, geophysics, decision theory, signal processing and control theory.

Computational Complexity

Author : Sanjeev Arora
Publisher : Cambridge University Press
ISBN 13 : 0521424267
Total Pages : 609 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Computational Complexity by : Sanjeev Arora

Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Oxford Users' Guide to Mathematics

Author : Eberhard Zeidler
Publisher : Oxford University Press
ISBN 13 : 0198507631
Total Pages : 1309 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Oxford Users' Guide to Mathematics by : Eberhard Zeidler

Download or read book Oxford Users' Guide to Mathematics written by Eberhard Zeidler and published by Oxford University Press. This book was released on 2004-08-19 with total page 1309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Oxford Users' Guide to Mathematics is one of the leading handbooks on mathematics available. It presents a comprehensive modern picture of mathematics and emphasises the relations between the different branches of mathematics, and the applications of mathematics in engineering and the natural sciences. The Oxford User's Guide covers a broad spectrum of mathematics starting with the basic material and progressing on to more advanced topics that have come to the fore in the last few decades. The book is organised into mathematical sub-disciplines including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimisation, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. The book is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics. It also includes a comprehensive bibliography of key contemporary literature as well as an extensive glossary and index. The wealth of material, reaching across all levels and numerous sub-disciplines, makes The Oxford User's Guide to Mathematics an invaluable reference source for students of engineering, mathematics, computer science, and the natural sciences, as well as teachers, practitioners, and researchers in industry and academia.

Verification and Validation in Scientific Computing

Author : William L. Oberkampf
Publisher : Cambridge University Press
ISBN 13 : 1139491768
Total Pages : 782 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Verification and Validation in Scientific Computing by : William L. Oberkampf

Download or read book Verification and Validation in Scientific Computing written by William L. Oberkampf and published by Cambridge University Press. This book was released on 2010-10-14 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.