Introduction To Interval Analysis
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Author | : Ramon E. Moore |
Publisher | : SIAM |
Total Pages | : 223 |
Release | : 2009-01-01 |
Genre | : Mathematics |
ISBN | : 089871771X |
Download Introduction to Interval Analysis Book in PDF, Epub and Kindle
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 |
Total Pages | : 136 |
Release | : 1979-01-01 |
Genre | : Mathematics |
ISBN | : 0898711614 |
Download Methods and Applications of Interval Analysis Book in PDF, Epub and Kindle
Mathematics of Computing -- Numerical Analysis.
Author | : Luc Jaulin |
Publisher | : Springer Science & Business Media |
Total Pages | : 382 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1447102495 |
Download Applied Interval Analysis Book in PDF, Epub and Kindle
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 | : Philipp Meisen |
Publisher | : Springer |
Total Pages | : 250 |
Release | : 2016-09-28 |
Genre | : Computers |
ISBN | : 3658157283 |
Download Analyzing Time Interval Data Book in PDF, Epub and Kindle
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 | : Eldon Hansen |
Publisher | : CRC Press |
Total Pages | : 528 |
Release | : 2003-12-19 |
Genre | : Mathematics |
ISBN | : 9780203026922 |
Download Global Optimization Using Interval Analysis Book in PDF, Epub and Kindle
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 | : Günter Mayer |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 625 |
Release | : 2017-04-10 |
Genre | : Mathematics |
ISBN | : 3110498057 |
Download Interval Analysis Book in PDF, Epub and Kindle
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 | : Gotz Alefeld |
Publisher | : Academic Press |
Total Pages | : 352 |
Release | : 2012-12-02 |
Genre | : Mathematics |
ISBN | : 0080916368 |
Download Introduction to Interval Computation Book in PDF, Epub and Kindle
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 | : A. Neumaier |
Publisher | : Cambridge University Press |
Total Pages | : 275 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 052133196X |
Download Interval Methods for Systems of Equations Book in PDF, Epub and Kindle
Mathematics of Computing -- Numerical Analysis.
Author | : Pierre-Jean Meyer |
Publisher | : Springer Nature |
Total Pages | : 115 |
Release | : 2021-01-20 |
Genre | : Technology & Engineering |
ISBN | : 303065110X |
Download Interval Reachability Analysis Book in PDF, Epub and Kindle
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 | : Andrew Browder |
Publisher | : Springer Science & Business Media |
Total Pages | : 348 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461207150 |
Download Mathematical Analysis Book in PDF, Epub and Kindle
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.