Applied 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 : 2001-08-30
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 2001-08-30 with Computers categories.
CD-ROM contains: trial version of Sun Microsystems' Forte Developer 6 for use with Solaris SPARC Platform Edition 2.6, 2.7 and 2.8.
Applied Interval Analysis
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Author : Luc Jaulin
language : en
Publisher:
Release Date : 2001-09-06
Applied Interval Analysis written by Luc Jaulin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-06 with categories.
This book is about guaranteed numerical methods based on interval analysis for approximating sets, and about the application of these methods to vast classes of engineering problems. Guaranteed means here that inner and outer approximations of the sets of interest are obtained, which can be made as precise as desired, at the cost of increasing the computational effort. It thus becomes possible to achieve tasks still thought by many to be out of the reach of numerical methods, such as finding all solutions of sets of non-linear equations and inequality or all global optimizers of possibly multi-modal criteria. The basic methodology is explained as simply as possible, in a concrete and readily applicable way, with a large number of figures and illustrative examples. Some of the techniques reported appear in book format for the first time. The ability of the approach advocated here to solve non-trivial engineering problems is demonstrated through examples drawn from the fields of parameter and state estimation, robust control and robotics. Enough detail is provided to allow readers with other applications in mind to grasp their significance. An in-depth treatment of implementation issues facilitates the understanding and use of freely available software that makes interval computation about as easy as computation with floating-point numbers. The reader is even given the basic information needed to build his or her own C++ interval library.
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 . . .
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 A New Tool For Applied Mathematics
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Author : L. B. Rall
language : en
Publisher:
Release Date : 1981
Interval Analysis A New Tool For Applied Mathematics written by L. B. Rall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Interval arithmetic has been found to be useful in numerical analysis as an automatic means to bound data, truncation, and roundoff errors in computations. Now that the speed of microprogrammed interval arithmetic approaches that of standard floating-point operations, a wider range of application to engineering and other problems has become feasible. Since, in many practical situations, data are only known to lie within intervals and only ranges of values are sought as satisfactory answers, straightforward interval computation can yield the desired results. Examples of this type of application are worst-case analysis of the stability of structures and the performance of electrical circuits. The recently developed theory of integration of interval functions also bears directly on the problems of solution of integral equations and the minimization of functionals defined in terms of integrals. Since certain chaotic phenomena, such as catastrophes and turbulence, are difficult to describe by single-valued functions, the introduction of interval functions and the corresponding analysis may lead to simpler models which will yield results of accuracy satisfactory for practical purposes.
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.
Mathematics of Computing -- Numerical Analysis.
Interval Analysis A Tool For Applied Mathematics
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Author : University of Wisconsin--Madison. Mathematics Research Center
language : en
Publisher:
Release Date : 1981
Interval Analysis A Tool For Applied Mathematics written by University of Wisconsin--Madison. Mathematics Research Center and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
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 Computers 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 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.
Applications Of Interval Computations
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Author : R. Baker Kearfott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Applications Of Interval Computations written by R. Baker Kearfott 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 2013-12-01 with Mathematics categories.
Primary Audience for the Book • Specialists in numerical computations who are interested in algorithms with automatic result verification. • Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc cessful applications. • Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli cations of numerical methods with automatic result verification, that were pre sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.