Interval Analysis
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Applied Interval Analysis
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Author : Luc Jaulin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Interval Analysis written by Luc Jaulin 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 Computers categories.
At the core of many engineering problems is the solution of sets of equa tions and inequalities, and the optimization of cost functions. Unfortunately, except in special cases, such as when a set of equations is linear in its un knowns or when a convex cost function has to be minimized under convex constraints, the results obtained by conventional numerical methods are only local and cannot be guaranteed. This means, for example, that the actual global minimum of a cost function may not be reached, or that some global minimizers of this cost function may escape detection. By contrast, interval analysis makes it possible to obtain guaranteed approximations of the set of all the actual solutions of the problem being considered. This, together with the lack of books presenting interval techniques in such a way that they could become part of any engineering numerical tool kit, motivated the writing of this book. The adventure started in 1991 with the preparation by Luc Jaulin of his PhD thesis, under Eric Walter's supervision. It continued with their joint supervision of Olivier Didrit's and Michel Kieffer's PhD theses. More than two years ago, when we presented our book project to Springer, we naively thought that redaction would be a simple matter, given what had already been achieved . . .
Methods And Applications Of Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher: SIAM
Release Date : 1979-01-01
Methods And Applications Of 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 1979-01-01 with Mathematics categories.
This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in 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.
Introduction To Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher: SIAM
Release Date : 2009-04-16
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 2009-04-16 with Mathematics categories.
An introduction to interval analysis for scientists and engineers interested in scientific computation, especially using INTLAB/MATLAB®.
Interval Analysis
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Author : Navid Razmjooy
language : en
Publisher: John Wiley & Sons
Release Date : 2023-12-27
Interval Analysis written by Navid Razmjooy 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 2023-12-27 with Technology & Engineering categories.
Interval Analysis An innovative and unique application of interval analysis to optimal control problems In Interval Analysis: Application in the Optimal Control Problems, celebrated researcher and engineer Dr. Navid Razmjooy delivers an expert discussion of the uncertainties in the analysis of optimal control problems. In the book, Dr. Razmjooy uses an open-ended approach to solving optimal control problems with indefinite intervals. Utilizing an extended, Runge-Kutta method, the author demonstrates how to accelerate its speed with the piecewise function. You’ll find recursive methods used to achieve more compact answers, as well as how to solve optimal control problems using the interval Chebyshev’s function. The book also contains: A thorough introduction to common errors and mistakes, generating uncertainties in physical models Comprehensive explorations of the literature on the subject, including Hukurara’s derivatives Practical discussions of the interval analysis and its variants, including the classical (Minkowski) methods Complete treatments of existing control methods, including classic, conventional advanced, and robust control. Perfect for master’s and PhD students working on system uncertainties, Interval Analysis: Application in the Optimal Control Problems will also benefit researchers working in laboratories, universities, and research centers.
Analyzing Time Interval Data
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Author : Philipp Meisen
language : en
Publisher: Springer
Release Date : 2016-09-28
Analyzing Time Interval Data written by Philipp Meisen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-28 with Computers categories.
Philipp Meisen introduces a model, a query language, and a similarity measure enabling users to analyze time interval data. The introduced tools are combined to design and realize an information system. The presented system is capable of performing analytical tasks (avoiding any type of summarizability problems), providing insights, and visualizing results processing millions of intervals within milliseconds using an intuitive SQL-based query language. The heart of the solution is based on several bitmap-based indexes, which enable the system to handle huge amounts of time interval data.
Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher:
Release Date : 1966
Interval Analysis written by Ramon E. Moore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Computer programming categories.
Advances In Numerical Analysis Emphasizing Interval Data
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Author : Tofigh Allahviranloo
language : en
Publisher: CRC Press
Release Date : 2022-02-17
Advances In Numerical Analysis Emphasizing Interval Data written by Tofigh Allahviranloo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Technology & Engineering categories.
Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges. The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory. Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.
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
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.