Interval Methods For Systems Of Equations
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Interval Methods For Systems Of Equations
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Author : Arnold Neumaier
language : en
Publisher:
Release Date : 1990
Interval Methods For Systems Of Equations written by Arnold Neumaier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Equations categories.
An interval is a natural way of specifying a number that is specified only within certain tolerances. Interval analysis consists of the tools and methods needed to solve linear and nonlinear systems of equations in the presence of data uncertainties. Applications include the sensitivity analysis of solutions of equations depending on parameters, the solution of global nonlinear problems, and the verification of results obtained by finite-precision arithmetic. In this book emphasis is laid on those aspects of the theory which are useful in actual computations. On the other hand, the theory is developed with full mathematical rigour. In order to keep the book self-contained, various results from linear algebra (Perron-Frobenius theory, M- and H- matrices) and analysis (existence of solutions to nonlinear systems) are proved, often from a novel and more general viewpoint. An extensive bibliography is included.
Interval Methods For Solving Nonlinear Constraint Satisfaction Optimization And Similar Problems
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Author : Bartłomiej Jacek Kubica
language : en
Publisher: Springer
Release Date : 2019-03-08
Interval Methods For Solving Nonlinear Constraint Satisfaction Optimization And Similar Problems written by Bartłomiej Jacek Kubica and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-08 with Technology & Engineering categories.
This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals’ endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.
Interval Methods For Systems Of Equations
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Author : A. Neumaier
language : en
Publisher: Cambridge University Press
Release Date : 1990
Interval Methods For Systems Of Equations 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 1990 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Reliability In Computing
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Author : Ramon E. Moore
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Reliability In Computing written by Ramon E. Moore and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms. The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence. The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions. The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.
Introduction To Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher: SIAM
Release Date : 2009-01-01
Introduction To Interval Analysis written by Ramon E. Moore and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.
An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.
Interval Methods For Circuit Analysis
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Author : L. V. Kolev
language : en
Publisher: World Scientific
Release Date : 1993
Interval Methods For Circuit Analysis written by L. V. Kolev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Technology & Engineering categories.
Written by an electrical engineer this book presents a novel approach in electric circuit theory which is based on interval analysis ? an intensively developing branch or applied mathematics. Covering major topics in both circuit and system theory and their applications, it suggests a variety of methods that are suited for handling linear and nonlinear analysis problems in which some or all of the relevant data are given as intervals. Detailed algorithms of the interval methods presented are developed, enabling their easy implementation on computers. For the convenience of the reader a comprehensive survey of all the necessary interval analysis notions and techniques is provided in the introductory text. Most of the theoretical developments considered in the book are also clearly illustrated through numerical examples.
Interval Methods For Circuit Analysis
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Author : L Kolev
language : en
Publisher: World Scientific
Release Date : 1993-09-23
Interval Methods For Circuit Analysis written by L Kolev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-23 with Technology & Engineering categories.
Written by an electrical engineer this book presents a novel approach in electric circuit theory which is based on interval analysis — an intensively developing branch or applied mathematics. Covering major topics in both circuit and system theory and their applications, it suggests a variety of methods that are suited for handling linear and nonlinear analysis problems in which some or all of the relevant data are given as intervals. Detailed algorithms of the interval methods presented are developed, enabling their easy implementation on computers. For the convenience of the reader a comprehensive survey of all the necessary interval analysis notions and techniques is provided in the introductory text. Most of the theoretical developments considered in the book are also clearly illustrated through numerical examples.
Global Optimization Using Interval Analysis
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Author : Eldon Hansen
language : en
Publisher: CRC Press
Release Date : 2003-12-19
Global Optimization Using Interval Analysis written by Eldon Hansen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-19 with Mathematics categories.
Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.
Interval Methods For Uncertain Power System Analysis
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Author : Alfredo Vaccaro
language : en
Publisher: John Wiley & Sons
Release Date : 2023-07-12
Interval Methods For Uncertain Power System Analysis written by Alfredo Vaccaro and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-12 with Technology & Engineering categories.
Interval Methods for Uncertain Power System Analysis In Interval Methods for Uncertain Power System Analysis, accomplished engineer Dr. Alfredo Vaccaro delivers a comprehensive discussion of the mathematical foundations of range analysis and its application to solving traditional power system operation problems in the presence of strong and correlated uncertainties. The book explores highly relevant topics in the area, from interval methods for uncertainty representation and management to a variety of application examples. The author offers readers the latest methodological breakthroughs and roadmaps to implementing the mathematics discussed within, as well as best practices commonly employed across the industry. Interval Methods for Uncertain Power System Analysis includes examinations of linear and non-linear equations, as well as: A thorough introduction to reliable computing, including discussions of interval arithmetic and interval-based operators Comprehensive explorations of uncertain power flow analysis, including discussions of problem formulation and sources of uncertainty in power flow analysis In-depth examinations of uncertain optimal power flow analysis Fulsome discussions of uncertain small signal stability analysis, including treatments of how to compute eigenvalues of uncertain matrices Perfect for engineers working in power flow and optimal power flow analyses, optimization theory, and computer aided simulation, Interval Methods for Uncertain Power System Analysis will also earn a place in the libraries of researchers and graduate students studying decision making under uncertainty in power systems operation.
Global Optimization Using Interval Analysis
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Author : Eldon Hansen
language : en
Publisher: CRC Press
Release Date : 2003-12-19
Global Optimization Using Interval Analysis written by Eldon Hansen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-19 with Mathematics categories.
Employing a closed set-theoretic foundation for interval computations, Global Optimization Using Interval Analysis simplifies algorithm construction and increases generality of interval arithmetic. This Second Edition contains an up-to-date discussion of interval methods for solving systems of nonlinear equations and global optimization problems. It expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance. Provided algorithms are guaranteed to find and bound all solutions to these problems despite bounded errors in data, in approximations, and from use of rounded arithmetic.