Applications Of Interval Computations

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Theories of Interval Arithmetic

Author : Hend Dawood
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 3846501549
Total Pages : 128 pages
Book Rating : 4.8/5 (465 download)

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Book Synopsis Theories of Interval Arithmetic by : Hend Dawood

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

Methods and Applications of Interval Analysis

Author : Ramon E. Moore
Publisher : SIAM
ISBN 13 : 9781611970906
Total Pages : 190 pages
Book Rating : 4.9/5 (79 download)

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Book Synopsis Methods and Applications of Interval Analysis by : Ramon E. Moore

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.

Introduction to Interval Analysis

Author : Ramon E. Moore
Publisher : SIAM
ISBN 13 : 089871771X
Total Pages : 223 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Introduction to Interval Analysis by : Ramon E. Moore

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.

Applications of Interval Computations

Author : R. Baker Kearfott
Publisher : Boom Koninklijke Uitgevers
ISBN 13 : 9780792338475
Total Pages : 460 pages
Book Rating : 4.3/5 (384 download)

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Book Synopsis Applications of Interval Computations by : R. Baker Kearfott

Download or read book Applications of Interval Computations written by R. Baker Kearfott and published by Boom Koninklijke Uitgevers. This book was released on 1996-01-31 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a February 1994 international workshop held in El Paso, Texas, survey industrial applications of numerical analysis with automatic result verification, and of interval representation of data. After an introductory chapter explaining the content of the papers in terminology accessible to mathematically literate graduate students, chapters describe applications such as economic input-output models; quality control in manufacturing design; and medical expert systems, focusing on dealing with problems such as overestimation. Other topics include branch and bound algorithms for global optimization; fuzzy logic; and constraint propagation. For students and researchers interested in automatic result verification. Annotation copyright by Book News, Inc., Portland, OR

Applied Interval Analysis

Author : Luc Jaulin
Publisher : Springer Science & Business Media
ISBN 13 : 1447102495
Total Pages : 382 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Applied Interval Analysis by : Luc Jaulin

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 . . .

Applications of Interval Computations

Author : R. Baker Kearfott
Publisher : Springer Science & Business Media
ISBN 13 : 1461334403
Total Pages : 435 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Applications of Interval Computations by : R. Baker Kearfott

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.

Interval Methods for Systems of Equations

Author : A. Neumaier
Publisher : Cambridge University Press
ISBN 13 : 052133196X
Total Pages : 275 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Interval Methods for Systems of Equations by : A. Neumaier

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.

Computational Complexity and Feasibility of Data Processing and Interval Computations

Author : V. Kreinovich
Publisher : Springer Science & Business Media
ISBN 13 : 1475727933
Total Pages : 460 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Computational Complexity and Feasibility of Data Processing and Interval Computations by : V. Kreinovich

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.

Interval Reachability Analysis

Author : Pierre-Jean Meyer
Publisher : Springer Nature
ISBN 13 : 303065110X
Total Pages : 115 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Interval Reachability Analysis by : Pierre-Jean Meyer

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.

Global Optimization Using Interval Analysis

Author : Eldon Hansen
Publisher : CRC Press
ISBN 13 : 9780203026922
Total Pages : 528 pages
Book Rating : 4.0/5 (269 download)

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Book Synopsis Global Optimization Using Interval Analysis by : Eldon Hansen

Download or read book Global Optimization Using Interval Analysis written by Eldon Hansen and published by CRC Press. This book was released on 2003-12-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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-Censored Time-to-Event Data

Author : Ding-Geng (Din) Chen
Publisher : CRC Press
ISBN 13 : 1466504250
Total Pages : 435 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Interval-Censored Time-to-Event Data by : Ding-Geng (Din) Chen

Download or read book Interval-Censored Time-to-Event Data written by Ding-Geng (Din) Chen and published by CRC Press. This book was released on 2012-07-19 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interval-Censored Time-to-Event Data: Methods and Applications collects the most recent techniques, models, and computational tools for interval-censored time-to-event data. Top biostatisticians from academia, biopharmaceutical industries, and government agencies discuss how these advances are impacting clinical trials and biomedical research. Divided into three parts, the book begins with an overview of interval-censored data modeling, including nonparametric estimation, survival functions, regression analysis, multivariate data analysis, competing risks analysis, and other models for interval-censored data. The next part presents interval-censored methods for current status data, Bayesian semiparametric regression analysis of interval-censored data with monotone splines, Bayesian inferential models for interval-censored data, an estimator for identifying causal effect of treatment, and consistent variance estimation for interval-censored data. In the final part, the contributors use Monte Carlo simulation to assess biases in progression-free survival analysis as well as correct bias in interval-censored time-to-event applications. They also present adaptive decision making methods to optimize the rapid treatment of stroke, explore practical issues in using weighted logrank tests, and describe how to use two R packages. A practical guide for biomedical researchers, clinicians, biostatisticians, and graduate students in biostatistics, this volume covers the latest developments in the analysis and modeling of interval-censored time-to-event data. It shows how up-to-date statistical methods are used in biopharmaceutical and public health applications.

Geometric Computations with Interval and New Robust Methods

Author : H Ratschek
Publisher : Horwood Publishing
ISBN 13 : 9781898563976
Total Pages : 342 pages
Book Rating : 4.5/5 (639 download)

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Book Synopsis Geometric Computations with Interval and New Robust Methods by : H Ratschek

Download or read book Geometric Computations with Interval and New Robust Methods written by H Ratschek and published by Horwood Publishing. This book was released on 2003-12-15 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free. Familiarises the reader with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations Provides two effective methods for obtaining correct results in interval arithmetic and ESSA

Introduction to Interval Computation

Author : Gotz Alefeld
Publisher : Academic Press
ISBN 13 : 0080916368
Total Pages : 352 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Introduction to Interval Computation by : Gotz Alefeld

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.

Scientific Computing, Computer Arithmetic, and Validated Numerics

Author : Marco Nehmeier
Publisher : Springer
ISBN 13 : 3319317695
Total Pages : 291 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Scientific Computing, Computer Arithmetic, and Validated Numerics by : Marco Nehmeier

Download or read book Scientific Computing, Computer Arithmetic, and Validated Numerics written by Marco Nehmeier and published by Springer. This book was released on 2016-04-08 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post proceedings of the 16th International Symposium, SCAN 2014, held in Würzburg, Germany, in September 2014. The 22 full papers presented were carefully reviewed and selected from 60 submissions. The main concerns of research addressed by SCAN conferences are validation, verification or reliable assertions of numerical computations. Interval arithmetic and other treatments of uncertainty are developed as appropriate tools.

Soft Methods for Integrated Uncertainty Modelling

Author : Jonathan Lawry
Publisher : Springer Science & Business Media
ISBN 13 : 3540347771
Total Pages : 413 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Soft Methods for Integrated Uncertainty Modelling by : Jonathan Lawry

Download or read book Soft Methods for Integrated Uncertainty Modelling written by Jonathan Lawry and published by Springer Science & Business Media. This book was released on 2007-10-08 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of soft computing emerged in the early 1990s from the fuzzy systems c- munity, and refers to an understanding that the uncertainty, imprecision and ig- rance present in a problem should be explicitly represented and possibly even - ploited rather than either eliminated or ignored in computations. For instance, Zadeh de?ned ‘Soft Computing’ as follows: Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty and partial truth. In effect, the role model for soft computing is the human mind. Recently soft computing has, to some extent, become synonymous with a hybrid approach combining AI techniques including fuzzy systems, neural networks, and biologically inspired methods such as genetic algorithms. Here, however, we adopt a more straightforward de?nition consistent with the original concept. Hence, soft methods are understood as those uncertainty formalisms not part of mainstream s- tistics and probability theory which have typically been developed within the AI and decisionanalysiscommunity.Thesearemathematicallysounduncertaintymodelling methodologies which are complementary to conventional statistics and probability theory.

The End of Error

Author : John L. Gustafson
Publisher : CRC Press
ISBN 13 : 135166560X
Total Pages : 536 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis The End of Error by : John L. Gustafson

Download or read book The End of Error written by John L. Gustafson and published by CRC Press. This book was released on 2017-06-26 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Future of Numerical Computing Written by one of the foremost experts in high-performance computing and the inventor of Gustafson’s Law, The End of Error: Unum Computing explains a new approach to computer arithmetic: the universal number (unum). The unum encompasses all IEEE floating-point formats as well as fixed-point and exact integer arithmetic. This new number type obtains more accurate answers than floating-point arithmetic yet uses fewer bits in many cases, saving memory, bandwidth, energy, and power. A Complete Revamp of Computer Arithmetic from the Ground Up Richly illustrated in color, this groundbreaking book represents a fundamental change in how to perform calculations automatically. It illustrates how this novel approach can solve problems that have vexed engineers and scientists for decades, including problems that have been historically limited to serial processing. Suitable for Anyone Using Computers for Calculations The book is accessible to anyone who uses computers for technical calculations, with much of the book only requiring high school math. The author makes the mathematics interesting through numerous analogies. He clearly defines jargon and uses color-coded boxes for mathematical formulas, computer code, important descriptions, and exercises.

The Lognormality Principle And Its Applications In E-security, E-learning And E-health

Author : Rejean Plamondon
Publisher : World Scientific
ISBN 13 : 9811226849
Total Pages : 446 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis The Lognormality Principle And Its Applications In E-security, E-learning And E-health by : Rejean Plamondon

Download or read book The Lognormality Principle And Its Applications In E-security, E-learning And E-health written by Rejean Plamondon and published by World Scientific. This book was released on 2020-11-17 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compendium provides a detailed account of the lognormality principle characterizing the human motor behavior by summarizing a sound theoretical framework for modeling such a behavior, introducing the most recent algorithms for extracting the lognormal components of complex movements in 2, 2.5 and 3 dimensions. It also vividly reports the most advanced applications to handwriting analysis and recognition, signature and writer verification, gesture recognition and calligraphy generation, evaluation of motor skills, improvement/degradation with aging, handwriting learning, education and developmental deficits, prescreening of children with ADHD (Attention Development and Hyperactivity Disorder), monitoring of concussion recovery, diagnosis and monitoring of Alzheimer's and Parkinson's diseases and aging effects in speech and handwriting.The volume provides a unique and useful source of references on the lognormality principle, an update on the most recent advances and an outlook at the most promising future developments in e-Security, e-Learning and e-Health.