Interval Computations
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Introduction To Interval Computation
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Author : Gotz Alefeld
language : en
Publisher: Academic Press
Release Date : 2012-12-02
Introduction To Interval Computation written by Gotz Alefeld and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
This book is revised and expanded version of the original German text. The arrangement of the material and the structure are essentially unchanged. All remarks in the Preface to the German Edition regarding naming conventions for formulas, theorems, lemmas, and definitions are still valid as are those concerning the arrangement and choice of material.
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.
Theories Of Interval Arithmetic
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Author : Hend Dawood
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-10-07
Theories Of Interval Arithmetic written by Hend Dawood and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-07 with Mathematics categories.
Scientists are, all the time, in a struggle with uncertainty which is always a threat to a trustworthy scientific knowledge. A very simple and natural idea, to defeat uncertainty, is that of enclosing uncertain measured values in real closed intervals. On the basis of this idea, interval arithmetic is constructed. The idea of calculating with intervals is not completely new in mathematics: the concept has been known since Archimedes, who used guaranteed lower and upper bounds to compute his constant Pi. Interval arithmetic is now a broad field in which rigorous mathematics is associated with scientific computing. This connection makes it possible to solve uncertainty problems that cannot be efficiently solved by floating-point arithmetic. Today, application areas of interval methods include electrical engineering, control theory, remote sensing, experimental and computational physics, chaotic systems, celestial mechanics, signal processing, computer graphics, robotics, and computer-assisted proofs. The purpose of this book is to be a concise but informative introduction to the theories of interval arithmetic as well as to some of their computational and scientific applications. Editorial Reviews "This new book by Hend Dawood is a fresh introduction to some of the basics of interval computation. It stops short of discussing the more complicated subdivision methods for converging to ranges of values, however it provides a bit of perspective about complex interval arithmetic, constraint intervals, and modal intervals, and it does go into the design of hardware operations for interval arithmetic, which is something still to be done by computer manufacturers." - Ramon E. Moore, (The Founder of Interval Computations) Professor Emeritus of Computer and Information Science, Department of Mathematics, The Ohio State University, Columbus, U.S.A. "A popular math-oriented introduction to interval computations and its applications. This short book contains an explanation of the need for interval computations, a brief history of interval computations, and main interval computation techniques. It also provides an impressive list of main practical applications of interval techniques." - Vladik Kreinovich, (International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems) Professor of Computer Science, University of Texas at El Paso, El Paso, Texas, U.S.A. "I am delighted to see one more Egyptian citizen re-entering the field of interval mathematics invented in this very country thousands years ago." - Marek W. Gutowski, Institute of Physics, Polish Academy of Sciences, Warszawa, Poland
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®.
Complex Interval Arithmetic And Its Applications
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Author : Miodrag Petković
language : en
Publisher: John Wiley & Sons
Release Date : 1998
Complex Interval Arithmetic And Its Applications written by Miodrag Petković 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 1998 with Mathematics categories.
The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.
Interval Computations
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Author :
language : en
Publisher:
Release Date : 1993
Interval Computations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Interval analysis (Mathematics) categories.
Encyclopedia Of Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04
Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
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.
Interval Computations
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Author :
language : en
Publisher:
Release Date : 1991
Interval Computations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Interval analysis (Mathematics) categories.
Iutam Symposium On The Vibration Analysis Of Structures With Uncertainties
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Author : Alexander K. Belyaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-02
Iutam Symposium On The Vibration Analysis Of Structures With Uncertainties written by Alexander K. Belyaev 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 2010-12-02 with Technology & Engineering categories.
The Symposium was aimed at the theoretical and numerical problems involved in modelling the dynamic response of structures which have uncertain properties due to variability in the manufacturing and assembly process, with automotive and aerospace structures forming prime examples. It is well known that the difficulty in predicting the response statistics of such structures is immense, due to the complexity of the structure, the large number of variables which might be uncertain, and the inevitable lack of data regarding the statistical distribution of these variables. The Symposium participants presented the latest thinking in this very active research area, and novel techniques were presented covering the full frequency spectrum of low, mid, and high frequency vibration problems. It was demonstrated that for high frequency vibrations the response statistics can saturate and become independent of the detailed distribution of the uncertain system parameters. A number of presentations exploited this physical behaviour by using and extending methods originally developed in both phenomenological thermodynamics and in the fields of quantum mechanics and random matrix theory. For low frequency vibrations a number of presentations focussed on parametric uncertainty modelling (for example, probabilistic models, interval analysis, and fuzzy descriptions) and on methods of propagating this uncertainty through a large dynamic model in an effi cient way. At mid frequencies the problem is mixed, and various hybrid schemes were proposed. It is clear that a comprehensivesolution to the problem of predicting the vibration response of uncertain structures across the whole frequency range requires expertise across a wide range of areas (including probabilistic and non-probabilistic methods, interval and info-gap analysis, statistical energy analysis, statistical thermodynamics, random wave approaches, and large scale computations) and this IUTAM symposium presented a unique opportunity to bring together outstanding international experts in these fields.