Perspectives On Enclosure Methods
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Perspectives On Enclosure Methods
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Author : Ulrich Kulisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Perspectives On Enclosure Methods written by Ulrich Kulisch 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.
Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.
Formal Modeling And Analysis Of Timed Systems
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Author : Alessandro Abate
language : en
Publisher: Springer
Release Date : 2017-09-01
Formal Modeling And Analysis Of Timed Systems written by Alessandro Abate and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-01 with Computers categories.
This book constitutes the refereed proceedings of the 15th International Conference on Formal Modeling and Analysis of Timed Systems, FORMATS 2017, held in Berlin, Germany, in September 2017. The aim of FORMATS is to promote the study of fundamental and practical aspects of timed systems, and to bring together researchers from different disciplines that share interests in modelling and analysis of timed systems and, as a generalization, hybrid systems.
Advanced Arithmetic For The Digital Computer
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Author : Ulrich W. Kulisch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-07
Advanced Arithmetic For The Digital Computer written by Ulrich W. Kulisch 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 2012-09-07 with Mathematics categories.
The number one requirement for computer arithmetic has always been speed. It is the main force that drives the technology. With increased speed larger problems can be attempted. To gain speed, advanced processors and pro gramming languages offer, for instance, compound arithmetic operations like matmul and dotproduct. But there is another side to the computational coin - the accuracy and reliability of the computed result. Progress on this side is very important, if not essential. Compound arithmetic operations, for instance, should always deliver a correct result. The user should not be obliged to perform an error analysis every time a compound arithmetic operation, implemented by the hardware manufacturer or in the programming language, is employed. This treatise deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic extends the accuracy of the elementary floating-point operations, for instance, as defined by the IEEE arithmetic standard, to all operations in the usual product spaces of computation: the complex numbers, the real and complex intervals, and the real and complex vectors and matrices and their interval counterparts. The implementation of advanced computer arithmetic by fast hardware is examined in this book. Arithmetic units for its elementary components are described. It is shown that the requirements for speed and for reliability do not conflict with each other. Advanced computer arithmetic is superior to other arithmetic with respect to accuracy, costs, and speed.
Interval Analysis
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Author : Günter Mayer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-10
Interval Analysis written by Günter Mayer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-10 with Mathematics categories.
This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals
Modeling Design And Simulation Of Systems With Uncertainties
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Author : Andreas Rauh
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-06
Modeling Design And Simulation Of Systems With Uncertainties written by Andreas Rauh 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 2011-06-06 with Technology & Engineering categories.
To describe the true behavior of most real-world systems with sufficient accuracy, engineers have to overcome difficulties arising from their lack of knowledge about certain parts of a process or from the impossibility of characterizing it with absolute certainty. Depending on the application at hand, uncertainties in modeling and measurements can be represented in different ways. For example, bounded uncertainties can be described by intervals, affine forms or general polynomial enclosures such as Taylor models, whereas stochastic uncertainties can be characterized in the form of a distribution described, for example, by the mean value, the standard deviation and higher-order moments. The goal of this Special Volume on Modeling, Design, and Simulation of Systems with Uncertainties is to cover modern methods for dealing with the challenges presented by imprecise or unavailable information. All contributions tackle the topic from the point of view of control, state and parameter estimation, optimization and simulation. Thematically, this volume can be divided into two parts. In the first we present works highlighting the theoretic background and current research on algorithmic approaches in the field of uncertainty handling, together with their reliable software implementation. The second part is concerned with real-life application scenarios from various areas including but not limited to mechatronics, robotics, and biomedical engineering.
Acta Numerica 2004 Volume 13
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03
Acta Numerica 2004 Volume 13 written by Arieh Iserles 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 2004-06-03 with Juvenile Nonfiction categories.
An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.
Positive Systems Theory And Applications
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Author : Luca Benvenuti
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-25
Positive Systems Theory And Applications written by Luca Benvenuti 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 2003-07-25 with Technology & Engineering categories.
The proceedings of the First Multidisciplinary International Symposium on Positive Systems Theory and Applications (POSTA 2003) held in Rome, Italy, August 28-30, 2003. Positive Systems are systems in which the relevant variables assume nonnegative values. These systems are quite common in applications where variables represent positive quantities such as populations, goods, money, time, data packets flowing in a network, densities of chemical species, probabilities, etc. The aim of the symposium was to join together researchers working in the different areas related to positive systems such as telecommunications, economy, biomedicine, chemistry and physics in order to provide a multidisciplinary forum where they have the opportunity to exchange ideas and compare results in a unifying framework.
Reliable Implementation Of Real Number Algorithms Theory And Practice
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Author : Peter Hertling
language : en
Publisher: Springer
Release Date : 2008-08-06
Reliable Implementation Of Real Number Algorithms Theory And Practice written by Peter Hertling and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-06 with Computers categories.
A large amount of the capacity of today’s computers is used for computations that can be described as computations involving real numbers. In this book, the focus is on a problem arising particularly in real number computations: the problem of veri?edor reliablecomputations. Since real numbersare objects c- taining an in?nite amount of information, they cannot be represented precisely on a computer. This leads to the well-known problems caused by unveri?ed - plementations of real number algorithms using ?nite precision. While this is t- ditionally seen to be a problem in numerical mathematics, there are also several scienti?c communities in computer science that are dealing with this problem. This book is a follow-up of the Dagstuhl Seminar 06021 on “Reliable Imp- mentation of Real Number Algorithms: Theory and Practice,” which took place January 8–13, 2006. It was intended to stimulate an exchange of ideas between the di?erent communities that deal with the problem of reliable implementation of real number algorithms either from a theoretical or from a practical point of view. Forty-eight researchers from many di?erent countries and many di?erent disciplines gathered in the castle of Dagstuhl to exchange views and ideas, in a relaxed atmosphere. The program consisted of 35 talks of 30 minutes each, and of three evening sessions with additional presentations and discussions. There were also lively discussions about di?erent theoretical models and practical - proaches for reliable real number computations.
System Identification Environmental Modelling And Control System Design
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Author : Liuping Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-20
System Identification Environmental Modelling And Control System Design written by Liuping Wang 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 2011-10-20 with Technology & Engineering categories.
This book is dedicated to Prof. Peter Young on his 70th birthday. Professor Young has been a pioneer in systems and control, and over the past 45 years he has influenced many developments in this field. This volume comprises a collection of contributions by leading experts in system identification, time-series analysis, environmetric modelling and control system design – modern research in topics that reflect important areas of interest in Professor Young’s research career. Recent theoretical developments in and relevant applications of these areas are explored treating the various subjects broadly and in depth. The authoritative and up-to-date research presented here will be of interest to academic researcher in control and disciplines related to environmental research, particularly those to with water systems. The tutorial style in which many of the contributions are composed also makes the book suitable as a source of study material for graduate students in those areas.
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.