Methods and Applications of Interval Analysis PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Methods and Applications of Interval Analysis PDF full book. Access full book title Methods and Applications of Interval Analysis by Ramon E. Moore. Download full books in PDF and EPUB format.
Author: Ramon E. Moore
Publisher: SIAM
ISBN: 9781611970906
Category : Mathematics
Languages : en
Pages : 190
Get Book
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: Ramon E. Moore
Publisher: SIAM
ISBN: 9781611970906
Category : Mathematics
Languages : en
Pages : 190
Get Book
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: Ramon E. Moore
Publisher: SIAM
ISBN: 089871771X
Category : Mathematics
Languages : en
Pages : 223
Get Book
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: Luc Jaulin
Publisher: Springer Science & Business Media
ISBN: 1447102495
Category : Computers
Languages : en
Pages : 382
Get Book
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: Pierre-Jean Meyer
Publisher: Springer Nature
ISBN: 303065110X
Category : Technology & Engineering
Languages : en
Pages : 115
Get Book
Book Description
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.
Author: Günter Mayer
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110498057
Category : Mathematics
Languages : en
Pages : 625
Get Book
Book Description
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
Author: Philipp Meisen
Publisher: Springer
ISBN: 3658157283
Category : Computers
Languages : en
Pages : 232
Get Book
Book Description
Philipp Meisen introduces a model, a query language, and a similarity measure enabling users to analyze time interval data. The introduced tools are combined to design and realize an information system. The presented system is capable of performing analytical tasks (avoiding any type of summarizability problems), providing insights, and visualizing results processing millions of intervals within milliseconds using an intuitive SQL-based query language. The heart of the solution is based on several bitmap-based indexes, which enable the system to handle huge amounts of time interval data.
Author: A. Neumaier
Publisher: Cambridge University Press
ISBN: 052133196X
Category : Mathematics
Languages : en
Pages : 275
Get Book
Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Eldon Hansen
Publisher: CRC Press
ISBN: 9780203026922
Category : Mathematics
Languages : en
Pages : 528
Get Book
Book Description
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.
Author: Tofigh Allahviranloo
Publisher: CRC Press
ISBN: 1000540251
Category : Technology & Engineering
Languages : en
Pages : 218
Get Book
Book Description
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.
Author: Jianguo Sun
Publisher: Springer
ISBN: 0387371192
Category : Mathematics
Languages : en
Pages : 304
Get Book
Book Description
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.
