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Author: R. Baker Kearfott
Publisher: Boom Koninklijke Uitgevers
ISBN: 9780792338475
Category : Computers
Languages : en
Pages : 460
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Book Description
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
Author: R. Baker Kearfott
Publisher: Boom Koninklijke Uitgevers
ISBN: 9780792338475
Category : Computers
Languages : en
Pages : 460
Get Book Here
Book Description
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
Author: R. Baker Kearfott
Publisher: Springer Science & Business Media
ISBN: 1461334403
Category : Mathematics
Languages : en
Pages : 435
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Book Description
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: Ramon E. Moore
Publisher: SIAM
ISBN: 089871771X
Category : Mathematics
Languages : en
Pages : 223
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Book Description
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: Ramon E. Moore
Publisher: SIAM
ISBN: 9781611970906
Category : Mathematics
Languages : en
Pages : 190
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Book Description
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: H Ratschek
Publisher: Elsevier
ISBN: 0857099515
Category : Mathematics
Languages : en
Pages : 337
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Book Description
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
Author: V. Kreinovich
Publisher: Springer Science & Business Media
ISBN: 1475727933
Category : Mathematics
Languages : en
Pages : 460
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Book Description
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: Luc Jaulin
Publisher: Springer Science & Business Media
ISBN: 1447102495
Category : Computers
Languages : en
Pages : 382
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Book Description
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: Kalimuthu Krishnamoorthy
Publisher: John Wiley & Sons
ISBN: 0470473894
Category : Mathematics
Languages : en
Pages : 494
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Book Description
A modern and comprehensive treatment of tolerance intervals and regions The topic of tolerance intervals and tolerance regions has undergone significant growth during recent years, with applications arising in various areas such as quality control, industry, and environmental monitoring. Statistical Tolerance Regions presents the theoretical development of tolerance intervals and tolerance regions through computational algorithms and the illustration of numerous practical uses and examples. This is the first book of its kind to successfully balance theory and practice, providing a state-of-the-art treatment on tolerance intervals and tolerance regions. The book begins with the key definitions, concepts, and technical results that are essential for deriving tolerance intervals and tolerance regions. Subsequent chapters provide in-depth coverage of key topics including: Univariate normal distribution Non-normal distributions Univariate linear regression models Nonparametric tolerance intervals The one-way random model with balanced data The multivariate normal distribution The one-way random model with unbalanced data The multivariate linear regression model General mixed models Bayesian tolerance intervals A final chapter contains coverage of miscellaneous topics including tolerance limits for a ratio of normal random variables, sample size determination, reference limits and coverage intervals, tolerance intervals for binomial and Poisson distributions, and tolerance intervals based on censored samples. Theoretical explanations are accompanied by computational algorithms that can be easily replicated by readers, and each chapter contains exercise sets for reinforcement of the presented material. Detailed appendices provide additional data sets and extensive tables of univariate and multivariate tolerance factors. Statistical Tolerance Regions is an ideal book for courses on tolerance intervals at the graduate level. It is also a valuable reference and resource for applied statisticians, researchers, and practitioners in industry and pharmaceutical companies.
Author: Gotz Alefeld
Publisher: Academic Press
ISBN: 0080916368
Category : Mathematics
Languages : en
Pages : 352
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Book Description
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: William Q. Meeker
Publisher: John Wiley & Sons
ISBN: 0471687170
Category : Mathematics
Languages : en
Pages : 648
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Book Description
Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easy-to-apply format Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses. Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on: Likelihood-based statistical intervals Nonparametric bootstrap intervals Parametric bootstrap and other simulation-based intervals An introduction to Bayesian intervals Bayesian intervals for the popular binomial, Poisson and normal distributions Statistical intervals for Bayesian hierarchical models Advanced case studies, further illustrating the use of the newly described methods New technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information. Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.
