Applications Of Interval Computations

Author : Ramon E. Moore
Publisher : SIAM
ISBN 13 : 9781611970906
Total Pages : 190 pages
Book Rating : 4.03/5 ( download)

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Download or read book Methods and Applications of Interval Analysis written by Ramon E. Moore and published by SIAM. This book was released on 1979-01-01 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : R. Baker Kearfott
Publisher : Springer Science & Business Media
ISBN 13 : 1461334403
Total Pages : 435 pages
Book Rating : 4.08/5 ( download)

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Download or read book Applications of Interval Computations written by R. Baker Kearfott and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hend Dawood
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 3846501549
Total Pages : 128 pages
Book Rating : 4.42/5 ( download)

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Download or read book Theories of Interval Arithmetic written by Hend Dawood and published by LAP Lambert Academic Publishing. This book was released on 2011-10-07 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Luc Jaulin
Publisher : Springer Science & Business Media
ISBN 13 : 1447102495
Total Pages : 382 pages
Book Rating : 4.96/5 ( download)

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Download or read book Applied Interval Analysis written by Luc Jaulin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 . . .

Author : Ramon E. Moore
Publisher : SIAM
ISBN 13 : 089871771X
Total Pages : 223 pages
Book Rating : 4.16/5 ( download)

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Download or read book Introduction to Interval Analysis written by Ramon E. Moore and published by SIAM. This book was released on 2009-01-01 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : A. Neumaier
Publisher : Cambridge University Press
ISBN 13 : 052133196X
Total Pages : 275 pages
Book Rating : 4.68/5 ( download)

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Download or read book Interval Methods for Systems of Equations written by A. Neumaier and published by Cambridge University Press. This book was released on 1990 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Author : V. Kreinovich
Publisher : Springer Science & Business Media
ISBN 13 : 1475727933
Total Pages : 460 pages
Book Rating : 4.37/5 ( download)

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Download or read book Computational Complexity and Feasibility of Data Processing and Interval Computations written by V. Kreinovich and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeted audience • Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. • Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. • Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing.

Author : Gotz Alefeld
Publisher : Academic Press
ISBN 13 : 0080916368
Total Pages : 352 pages
Book Rating : 4.61/5 ( download)

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Download or read book Introduction to Interval Computation written by Gotz Alefeld and published by Academic Press. This book was released on 2012-12-02 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Miodrag Petković
Publisher : John Wiley & Sons
ISBN 13 : 9783527401345
Total Pages : 296 pages
Book Rating : 4.42/5 ( download)

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Download or read book Complex Interval Arithmetic and Its Applications written by Miodrag Petković and published by John Wiley & Sons. This book was released on 1998 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Pierre-Jean Meyer
Publisher : Springer Nature
ISBN 13 : 303065110X
Total Pages : 115 pages
Book Rating : 4.07/5 ( download)

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Download or read book Interval Reachability Analysis written by Pierre-Jean Meyer and published by Springer Nature. This book was released on 2021-01-20 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or ‘boxes’. It explains the importance of bounding trajectories for evaluating the robustness of systems in the face of parametric uncertainty, and for verification or control synthesis problems with respect to safety and reachability properties. The methods presented make use of: interval analysis; monotonicity theory; contraction theory; and data-driven techniques that sample trajectories. The methods are implemented in an accompanying open-source Toolbox for Interval Reachability Analysis. This brief provides a tutorial description of each method, focusing on the requirements and trade-offs relevant to the user, requiring only basic background on dynamical systems. The second part of the brief describes applications of interval reachability analysis. This makes the brief of interest to a wide range of academic researchers, graduate students, and practising engineers in the field of control and verification.