Interval Analysis

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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 . . .

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.

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.

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.

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.

Survival Analysis with Interval-Censored Data

Author : Kris Bogaerts
Publisher : CRC Press
ISBN 13 : 1351643053
Total Pages : 644 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Survival Analysis with Interval-Censored Data by : Kris Bogaerts

Download or read book Survival Analysis with Interval-Censored Data written by Kris Bogaerts and published by CRC Press. This book was released on 2017-11-20 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survival Analysis with Interval-Censored Data: A Practical Approach with Examples in R, SAS, and BUGS provides the reader with a practical introduction into the analysis of interval-censored survival times. Although many theoretical developments have appeared in the last fifty years, interval censoring is often ignored in practice. Many are unaware of the impact of inappropriately dealing with interval censoring. In addition, the necessary software is at times difficult to trace. This book fills in the gap between theory and practice. Features: -Provides an overview of frequentist as well as Bayesian methods. -Include a focus on practical aspects and applications. -Extensively illustrates the methods with examples using R, SAS, and BUGS. Full programs are available on a supplementary website. The authors: Kris Bogaerts is project manager at I-BioStat, KU Leuven. He received his PhD in science (statistics) at KU Leuven on the analysis of interval-censored data. He has gained expertise in a great variety of statistical topics with a focus on the design and analysis of clinical trials. Arnošt Komárek is associate professor of statistics at Charles University, Prague. His subject area of expertise covers mainly survival analysis with the emphasis on interval-censored data and classification based on longitudinal data. He is past chair of the Statistical Modelling Society and editor of Statistical Modelling: An International Journal. Emmanuel Lesaffre is professor of biostatistics at I-BioStat, KU Leuven. His research interests include Bayesian methods, longitudinal data analysis, statistical modelling, analysis of dental data, interval-censored data, misclassification issues, and clinical trials. He is the founding chair of the Statistical Modelling Society, past-president of the International Society for Clinical Biostatistics, and fellow of ISI and ASA.

The Statistical Analysis of Interval-censored Failure Time Data

Author : Jianguo Sun
Publisher : Springer
ISBN 13 : 0387371192
Total Pages : 304 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis The Statistical Analysis of Interval-censored Failure Time Data by : Jianguo Sun

Download or read book The Statistical Analysis of Interval-censored Failure Time Data written by Jianguo Sun and published by Springer. This book was released on 2007-05-26 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects and unifies statistical models and methods that have been proposed for analyzing interval-censored failure time data. It provides the first comprehensive coverage of the topic of interval-censored data and complements the books on right-censored data. The focus of the book is on nonparametric and semiparametric inferences, but it also describes parametric and imputation approaches. This book provides an up-to-date reference for people who are conducting research on the analysis of interval-censored failure time data as well as for those who need to analyze interval-censored data to answer substantive questions.

Advances in Numerical Analysis Emphasizing Interval Data

Author : Tofigh Allahviranloo
Publisher : CRC Press
ISBN 13 : 1000540251
Total Pages : 218 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Advances in Numerical Analysis Emphasizing Interval Data by : Tofigh Allahviranloo

Download or read book Advances in Numerical Analysis Emphasizing Interval Data written by Tofigh Allahviranloo and published by CRC Press. This book was released on 2022-02-18 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical analysis forms a cornerstone of numeric computing and optimization, in particular recently, interval numerical computations play an important role in these topics. The interest of researchers in computations involving uncertain data, namely interval data opens new avenues in coping with real-world problems and deliver innovative and efficient solutions. This book provides the basic theoretical foundations of numerical methods, discusses key technique classes, explains improvements and improvements, and provides insights into recent developments and challenges. The theoretical parts of numerical methods, including the concept of interval approximation theory, are introduced and explained in detail. In general, the key features of the book include an up-to-date and focused treatise on error analysis in calculations, in particular the comprehensive and systematic treatment of error propagation mechanisms, considerations on the quality of data involved in numerical calculations, and a thorough discussion of interval approximation theory. Moreover, this book focuses on approximation theory and its development from the perspective of linear algebra, and new and regular representations of numerical integration and their solutions are enhanced by error analysis as well. The book is unique in the sense that its content and organization will cater to several audiences, in particular graduate students, researchers, and practitioners.

Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis)

Author : G. Alefeld
Publisher : Springer Science & Business Media
ISBN 13 : 3709185777
Total Pages : 228 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis) by : G. Alefeld

Download or read book Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis) written by G. Alefeld and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Data Analysis, Classification, and Related Methods

Author : Henk A.L. Kiers
Publisher : Springer Science & Business Media
ISBN 13 : 3642597890
Total Pages : 428 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Data Analysis, Classification, and Related Methods by : Henk A.L. Kiers

Download or read book Data Analysis, Classification, and Related Methods written by Henk A.L. Kiers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers presented at the Seven~h Confer ence of the International Federation of Classification Societies (IFCS-2000), which was held in Namur, Belgium, July 11-14,2000. From the originally sub mitted papers, a careful review process involving two reviewers per paper, led to the selection of 65 papers that were considered suitable for publication in this book. The present book contains original research contributions, innovative ap plications and overview papers in various fields within data analysis, classifi cation, and related methods. Given the fast publication process, the research results are still up-to-date and coincide with their actual presentation at the IFCS-2000 conference. The topics captured are: • Cluster analysis • Comparison of clusterings • Fuzzy clustering • Discriminant analysis • Mixture models • Analysis of relationships data • Symbolic data analysis • Regression trees • Data mining and neural networks • Pattern recognition • Multivariate data analysis • Robust data analysis • Data science and sampling The IFCS (International Federation of Classification Societies) The IFCS promotes the dissemination of technical and scientific information data analysis, classification, related methods, and their applica concerning tions.

Interval Analysis

Author : Navid Razmjooy
Publisher : John Wiley & Sons
ISBN 13 : 1394190972
Total Pages : 212 pages
Book Rating : 4.3/5 (941 download)

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Book Synopsis Interval Analysis by : Navid Razmjooy

Download or read book Interval Analysis written by Navid Razmjooy and published by John Wiley & Sons. This book was released on 2024-01-04 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interval Analysis An innovative and unique application of interval analysis to optimal control problems In Interval Analysis: Application in the Optimal Control Problems, celebrated researcher and engineer Dr. Navid Razmjooy delivers an expert discussion of the uncertainties in the analysis of optimal control problems. In the book, Dr. Razmjooy uses an open-ended approach to solving optimal control problems with indefinite intervals. Utilizing an extended, Runge-Kutta method, the author demonstrates how to accelerate its speed with the piecewise function. You’ll find recursive methods used to achieve more compact answers, as well as how to solve optimal control problems using the interval Chebyshev’s function. The book also contains: A thorough introduction to common errors and mistakes, generating uncertainties in physical models Comprehensive explorations of the literature on the subject, including Hukurara’s derivatives Practical discussions of the interval analysis and its variants, including the classical (Minkowski) methods Complete treatments of existing control methods, including classic, conventional advanced, and robust control. Perfect for master’s and PhD students working on system uncertainties, Interval Analysis: Application in the Optimal Control Problems will also benefit researchers working in laboratories, universities, and research centers.

Interval Analysis

Author : Günter Mayer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110499460
Total Pages : 532 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Interval Analysis by : Günter Mayer

Download or read book Interval Analysis written by Günter Mayer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals

Modal Interval Analysis

Author : Miguel A. Sainz
Publisher : Springer
ISBN 13 : 3319017217
Total Pages : 316 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Modal Interval Analysis by : Miguel A. Sainz

Download or read book Modal Interval Analysis written by Miguel A. Sainz and published by Springer. This book was released on 2013-11-18 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals through the inclusion of the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equivalences, along with guidelines for arriving at these inclusions. Applications of these equivalences in different areas illustrate the obtained results. The book also presents a new interval object: marks, which aspire to be a new form of numerical treatment of errors in measurements and computations.

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.

Interval Methods for Circuit Analysis

Author :
Publisher :
ISBN 13 : 9814504106
Total Pages : pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Interval Methods for Circuit Analysis by :

Download or read book Interval Methods for Circuit Analysis written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interval Methods for Circuit Analysis

Author : L. V. Kolev
Publisher : World Scientific
ISBN 13 : 9789810214135
Total Pages : 328 pages
Book Rating : 4.2/5 (141 download)

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Book Synopsis Interval Methods for Circuit Analysis by : L. V. Kolev

Download or read book Interval Methods for Circuit Analysis written by L. V. Kolev and published by World Scientific. This book was released on 1993 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.