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Applied Interval Analysis
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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 . . .
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.
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.
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.
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.
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 2009-04-16 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to interval analysis for scientists and engineers interested in scientific computation, especially using INTLAB/MATLAB®.
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.
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.
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 135 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.
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.
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.
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
Book Synopsis Confirmatory Factor Analysis for Applied Research, Second Edition by : Timothy A. Brown
Download or read book Confirmatory Factor Analysis for Applied Research, Second Edition written by Timothy A. Brown and published by Guilford Publications. This book was released on 2015-01-07 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible book has established itself as the go-to resource on confirmatory factor analysis (CFA) for its emphasis on practical and conceptual aspects rather than mathematics or formulas. Detailed, worked-through examples drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology. The text shows how to formulate, program, and interpret CFA models using popular latent variable software packages (LISREL, Mplus, EQS, SAS/CALIS); understand the similarities ...
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.
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.
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.
Book Synopsis Parallel Processing and Applied Mathematics, Part II by : Roman Wyrzykowski
Download or read book Parallel Processing and Applied Mathematics, Part II written by Roman Wyrzykowski and published by Springer. This book was released on 2012-07-04 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume-set (LNCS 7203 and 7204) constitutes the refereed proceedings of the 9th International Conference on Parallel Processing and Applied Mathematics, PPAM 2011, held in Torun, Poland, in September 2011. The 130 revised full papers presented in both volumes were carefully reviewed and selected from numerous submissions. The papers address issues such as parallel/distributed architectures and mobile computing; numerical algorithms and parallel numerics; parallel non-numerical algorithms; tools and environments for parallel/distributed/grid computing; applications of parallel/distributed computing; applied mathematics, neural networks and evolutionary computing; history of computing.
