Topics In Validated Computations
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Topics In Validated Computations
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Author : Jürgen Herzberger
language : en
Publisher: Elsevier Publishing Company
Release Date : 1994
Topics In Validated Computations written by Jürgen Herzberger and has been published by Elsevier Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This text provides the interval analysis community with surveys of important recent developments in the creation of validated numerical algorithms. In addition, the publication informs the numerical analysts and appliers of numerical software about the enormous variety of problem-solving algorithms now available, even for sophisticated problems which were beyond reach at the beginning of research some two decades ago. Contributions are sourced from a variety of international experts and together these form a textbook collection of 14 non-overlapping multidisciplinary sections. in interval arithmetic, whilst the concluding chapter offers instructions on how to implement interval algorithms. Other problem areas addressed in the bulk of the volume include: systems of nonlinear equations, simultaneous methods for polynomial zeros, linear systems, matrix inversion, matrix eigenvalue problems, eigenvalues of selfadjoint problems, ODE's, PDE's, optimization, problems in engineering, and complexity considerations in linear interval problems.
Computational Methods In Transport Verification And Validation
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Author : Frank Graziani
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-09
Computational Methods In Transport Verification And Validation written by Frank Graziani 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 2008-08-09 with Science categories.
The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.
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.
Computer Simulation Validation
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Author : Claus Beisbart
language : en
Publisher: Springer
Release Date : 2019-04-09
Computer Simulation Validation written by Claus Beisbart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-09 with Computers categories.
This unique volume introduces and discusses the methods of validating computer simulations in scientific research. The core concepts, strategies, and techniques of validation are explained by an international team of pre-eminent authorities, drawing on expertise from various fields ranging from engineering and the physical sciences to the social sciences and history. The work also offers new and original philosophical perspectives on the validation of simulations. Topics and features: introduces the fundamental concepts and principles related to the validation of computer simulations, and examines philosophical frameworks for thinking about validation; provides an overview of the various strategies and techniques available for validating simulations, as well as the preparatory steps that have to be taken prior to validation; describes commonly used reference points and mathematical frameworks applicable to simulation validation; reviews the legal prescriptions, and the administrative and procedural activities related to simulation validation; presents examples of best practice that demonstrate how methods of validation are applied in various disciplines and with different types of simulation models; covers important practical challenges faced by simulation scientists when applying validation methods and techniques; offers a selection of general philosophical reflections that explore the significance of validation from a broader perspective. This truly interdisciplinary handbook will appeal to a broad audience, from professional scientists spanning all natural and social sciences, to young scholars new to research with computer simulations. Philosophers of science, and methodologists seeking to increase their understanding of simulation validation, will also find much to benefit from in the text.
Verification Validation And Predictive Capability In Computational Engineering And Physics
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Author :
language : en
Publisher:
Release Date : 2003
Verification Validation And Predictive Capability In Computational Engineering And Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with 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.
Computational Methods For Communication Science
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Author : Wouter van Atteveldt
language : en
Publisher: Routledge
Release Date : 2021-03-29
Computational Methods For Communication Science written by Wouter van Atteveldt and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-29 with Language Arts & Disciplines categories.
Computational Methods for Communication Science showcases the use of innovative computational methods in the study of communication. This book discusses the validity of using big data in communication science and showcases a number of new methods and applications in the fields of text and network analysis. Computational methods have the potential to greatly enhance the scientific study of communication because they allow us to move towards collaborative large-N studies of actual behavior in its social context. This requires us to develop new skills and infrastructure and meet the challenges of open, valid, reliable, and ethical "big data" research. This volume brings together a number of leading scholars in this emerging field, contributing to the increasing development and adaptation of computational methods in communication science. The chapters in this book were originally published as a special issue of the journal Communication Methods and Measures.
Numerical Methods And Applications
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Author : Todor Boyanov
language : en
Publisher: Springer
Release Date : 2007-05-15
Numerical Methods And Applications written by Todor Boyanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-15 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of NMA 2006 held in Borovets, Bulgaria. Coverage in the 84 revised full papers includes numerical methods for hyperbolic problems, robust preconditioning solution methods, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, and large-scale computations in environmental modeling.
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.
Validated Numerics
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Author : Warwick Tucker
language : en
Publisher: Princeton University Press
Release Date : 2023-06-06
Validated Numerics written by Warwick Tucker and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Computers categories.
A comprehensive, self-contained primer on validated numerics This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error—fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates
Accuracy And Reliability In Scientific Computing
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Author : Bo Einarsson
language : en
Publisher: SIAM
Release Date : 2005-01-01
Accuracy And Reliability In Scientific Computing written by Bo Einarsson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Science categories.
Numerical software is used to test scientific theories, design airplanes and bridges, operate manufacturing lines, control power plants and refineries, analyze financial derivatives, identify genomes, and provide the understanding necessary to derive and analyze cancer treatments. Because of the high stakes involved, it is essential that results computed using software be accurate, reliable, and robust. Unfortunately, developing accurate and reliable scientific software is notoriously difficult. This book investigates some of the difficulties related to scientific computing and provides insight into how to overcome them and obtain dependable results. The tools to assess existing scientific applications are described, and a variety of techniques that can improve the accuracy and reliability of newly developed applications is discussed. Accuracy and Reliability in Scientific Computing can be considered a handbook for improving the quality of scientific computing. It will help computer scientists address the problems that affect software in general as well as the particular challenges of numerical computation: approximations occurring at all levels, continuous functions replaced by discretized versions, infinite processes replaced by finite ones, and real numbers replaced by finite precision numbers. Divided into three parts, it starts by illustrating some of the difficulties in producing robust and reliable scientific software. Well-known cases of failure are reviewed and the what and why of numerical computations are considered. The second section describes diagnostic tools that can be used to assess the accuracy and reliability of existing scientific applications. In the last section, the authors describe a variety of techniques that can be employed to improve the accuracy and reliability of newly developed scientific applications. The authors of the individual chapters are international experts, many of them members of the IFIP Working Group on Numerical Software.