Validation Numerics
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Validation Numerics
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Author : R. Albrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Validation Numerics written by R. Albrecht 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 2012-12-06 with Mathematics categories.
The articles in this book give a comprehensive overview on the whole field of validated numerics. The problems covered include simultaneous systems of linear and nonlinear equations, differential and integral equations and certain applications from technical sciences. Furthermore some papers which improve the tools are included. The book is a must for scientists working in numerical analysis, computer science and in technical fields.
Numerical Validation In Current Hardware Architectures
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Author : Annie A.M. Cuyt
language : en
Publisher: Springer
Release Date : 2009-04-28
Numerical Validation In Current Hardware Architectures written by Annie A.M. Cuyt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-28 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the Dagstuhl Seminar 08021 on Numerical Validation in Current Hardware Architectures held at Dagstuhl Castle, Germany, in January 2008. The 16 revised full papers presented were selected during two rounds of reviewing and improvements. The papers are organized in topical sections on languages, software systems and tools, new verification techniques based on interval arithmetic, applications in science and engineering, and novel approaches to verification.
Scientific Computing Validated Numerics Interval Methods
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Author : Walter Krämer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Scientific Computing Validated Numerics Interval Methods written by Walter Krämer 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 2013-04-17 with Computers categories.
Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.
Scientific Computing Computer Arithmetic And Validated Numerics
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Author : Marco Nehmeier
language : en
Publisher: Springer
Release Date : 2016-04-08
Scientific Computing Computer Arithmetic And Validated Numerics written by Marco Nehmeier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-08 with Computers categories.
This book constitutes the refereed post proceedings of the 16th International Symposium, SCAN 2014, held in Würzburg, Germany, in September 2014. The 22 full papers presented were carefully reviewed and selected from 60 submissions. The main concerns of research addressed by SCAN conferences are validation, verification or reliable assertions of numerical computations. Interval arithmetic and other treatments of uncertainty are developed as appropriate tools.
Self Validating Numerics For Function Space Problems
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Author : Edgar W. Kaucher
language : en
Publisher: Elsevier
Release Date : 2014-06-20
Self Validating Numerics For Function Space Problems written by Edgar W. Kaucher and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-20 with Mathematics categories.
Self-Validating Numerics for Function Space Problems describes the development of computational methods for solving function space problems, including differential, integral, and function equations. This seven-chapter text highlights three approaches, namely, the E-methods, ultra-arithmetic, and computer arithmetic. After a brief overview of the different self-validating approaches, this book goes on introducing the mathematical preliminaries consisting principally of fixed-point theorems and the computational context for the development of validating methods in function spaces. The subsequent chapters deals with the development and application of point of view of ultra-arithmetic and the constructs of function-space arithmetic spaces, such as spaces, bases, rounding, and approximate operations. These topics are followed by discussion of the iterative residual correction methods for function problems and the requirements of a programming language needed to make the tools and constructs of the methodology available in actual practice on a computer. The last chapter describes the techniques for adapting the methodologies to a computer, including the self-validating results for specific problems. This book will prove useful to mathematicians and advance mathematics students.
Verification Validation And Predictive Capability In Computational Engineering And Physics
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Author : William L. Oberkampf
language : en
Publisher:
Release Date : 2003
Verification Validation And Predictive Capability In Computational Engineering And Physics written by William L. Oberkampf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Computer simulation categories.
Developers of computer codes, analysts who use the codes, and decision makers who rely on the results of the analyses face a critical question: How should confidence in modeling and simulation be critically assessed? Verification and validation (V & V) of computational simulations are the primary methods for building and quantifying this confidence. Briefly, verification is the assessment of the accuracy of the solution to a computational model. Validation is the assessment of the accuracy of a computational simulation by comparison with experimental data. In verification, the relationship of the simulation to the real world is not an issue. In validation, the relationship between computation and the real world, i.e., experimental data, is the issue. This paper presents our viewpoint of the state of the art in V & V in computational physics. (In this paper we refer to all fields of computational engineering and physics, e.g., computational fluid dynamics, computational solid mechanics, structural dynamics, shock wave physics, computational chemistry, etc., as computational physics.) We do not provide a comprehensive review of the multitudinous contributions to V & V, although we do reference a large number of previous works from many fields. We have attempted to bring together many different perspectives on V & V, highlight those perspectives that are effective from a practical engineering viewpoint, suggest future research topics, and discuss key implementation issues that are necessary to improve the effectiveness of V & V. We describe our view of the framework in which predictive capability relies on V & V, as well as other factors that affect predictive capability. Our opinions about the research needs and management issues in V & V are very practical: What methods and techniques need to be developed and what changes in the views of management need to occur to increase the usefulness, reliability, and impact of computational physics for decision making about engineering systems? We review the state of the art in V & V over a wide range of topics, for example, prioritization of V & V activities using the Phenomena Identification and Ranking Table (PIRT), code verification, software quality assurance (SQA), numerical error estimation, hierarchical experiments for validation, characteristics of validation experiments, the need to perform nondeterministic computational simulations in comparisons with experimental data, and validation metrics. We then provide an extensive discussion of V & V research and implementation issues that we believe must be addressed for V & V to be more effective in improving confidence in computational predictive capability. Some of the research topics addressed are development of improved procedures for the use of the PIRT for prioritizing V & V activities, the method of manufactured solutions for code verification, development and use of hierarchical validation diagrams, and the construction and use of validation metrics incorporating statistical measures. Some of the implementation topics addressed are the needed management initiatives to better align and team computationalists and experimentalists in conducting validation activities, the perspective of commercial software companies, the key role of analysts and decision makers as code customers, obstacles to the improved effectiveness of V & V, effects of cost and schedule constraints on practical applications in industrial settings, and the role of engineering standards committees in documenting best practices for V & V.
Introduction To Numerical Analysis
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Author : A. Neumaier
language : en
Publisher: Cambridge University Press
Release Date : 2001-10
Introduction To Numerical Analysis written by A. Neumaier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10 with Mathematics categories.
This textbook provides an introduction to constructive methods that provide accurate approximations to the solution of numerical problems using MATLAB.
Numerical Computation Of Internal And External Flows The Fundamentals Of Computational Fluid Dynamics
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Author : Charles Hirsch
language : en
Publisher: Elsevier
Release Date : 2007-07-18
Numerical Computation Of Internal And External Flows The Fundamentals Of Computational Fluid Dynamics written by Charles Hirsch and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-18 with Science categories.
The second edition of this book is a self-contained introduction to computational fluid dynamics (CFD). It covers the fundamentals of the subject and is ideal as a text or a comprehensive reference to CFD theory and practice. - New approach takes readers seamlessly from first principles to more advanced and applied topics. - Presents the essential components of a simulation system at a level suitable for those coming into contact with CFD for the first time, and is ideal for those who need a comprehensive refresher on the fundamentals of CFD. - Enhanced pedagogy features chapter objectives, hands-on practice examples and end of chapter exercises. - Extended coverage of finite difference, finite volume and finite element methods. - New chapters include an introduction to grid properties and the use of grids in practice. - Includes material on 2-D inviscid, potential and Euler flows, 2-D viscous flows and Navier-Stokes flows to enable the reader to develop basic CFD simulations. - Includes best practice guidelines for applying existing commercial or shareware CFD tools.
Parallel Processing And Applied Mathematics
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Author : Roman Wyrzykowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-26
Parallel Processing And Applied Mathematics written by Roman Wyrzykowski 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 2004-04-26 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Parallel Processing and Applied Mathematics, PPAM 2003, held in Czestochowa, Poland, in September 2003. The 149 papers presented were carefully selected and improved during two rounds of reviewing and revision. The papers are organized in topical sections on parallel and distributed architectures, scheduling and load balancing, performance analysis and prediction, parallel and distributed non-numerical algorithms, parallel and distributed programming, tools and environments, applications, evolutionary computing, soft computing data and knowledge management, numerical methods and their applications, multi-dimensional systems, grid computing, heterogeneous platforms, high performance numerical computation, large-scale scientific computation, and bioinformatics applications.
Numerical Analysis
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Author : Jan Awrejcewicz
language : en
Publisher: BoD – Books on Demand
Release Date : 2011-09-09
Numerical Analysis written by Jan Awrejcewicz and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Computers categories.
Numerical Analysis - Theory and Application is an edited book divided into two parts: Part I devoted to Theory, and Part II dealing with Application. The presented book is focused on introducing theoretical approaches of numerical analysis as well as applications of various numerical methods to either study or solving numerous theoretical and engineering problems. Since a large number of pure theoretical research is proposed as well as a large amount of applications oriented numerical simulation results are given, the book can be useful for both theoretical and applied research aimed on numerical simulations. In addition, in many cases the presented approaches can be applied directly either by theoreticians or engineers.