Interval Mathematics

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Interval Mathematics 1980

Author : Karl L. E. Nickel
Publisher : Elsevier
ISBN 13 : 1483273849
Total Pages : 571 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Interval Mathematics 1980 by : Karl L. E. Nickel

Download or read book Interval Mathematics 1980 written by Karl L. E. Nickel and published by Elsevier. This book was released on 2014-05-10 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interval Mathematics 1980 contains the proceedings of an International Symposium on Interval Mathematics held in Germany on May 27-31, 1980. The book introduces the reader to some of the most important work done in the field of interval mathematics and its application to computing. Topics covered range from purely theoretical to computational methods and computer architecture. Comprised of 41 chapters, this book begins with an overview of set functions and their applications, followed by a discussion on global constrained optimization using interval analysis. A model for the propagation of rounding error in floating arithmetic is then presented, and the importance of 3-valued notions for interval mathematics is highlighted. Subsequent chapters focus on the transformation of interval programs into convergent interval programs; specifications for interval programming languages; interval contractions for the solution of integral equations; and mean convergence enclosing of solutions of operator equations with convex and inverse monotonic operators. This monograph will be of value to both students and specialists in the fields of mathematics and computer science.

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 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.

Theories of Interval Arithmetic

Author : Hend Dawood
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 3846501549
Total Pages : 128 pages
Book Rating : 4.8/5 (465 download)

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Book Synopsis Theories of Interval Arithmetic by : Hend Dawood

Download or read book Theories of Interval Arithmetic written by Hend Dawood and published by LAP Lambert Academic Publishing. This book was released on 2011-10-07 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists are, all the time, in a struggle with uncertainty which is always a threat to a trustworthy scientific knowledge. A very simple and natural idea, to defeat uncertainty, is that of enclosing uncertain measured values in real closed intervals. On the basis of this idea, interval arithmetic is constructed. The idea of calculating with intervals is not completely new in mathematics: the concept has been known since Archimedes, who used guaranteed lower and upper bounds to compute his constant Pi. Interval arithmetic is now a broad field in which rigorous mathematics is associated with scientific computing. This connection makes it possible to solve uncertainty problems that cannot be efficiently solved by floating-point arithmetic. Today, application areas of interval methods include electrical engineering, control theory, remote sensing, experimental and computational physics, chaotic systems, celestial mechanics, signal processing, computer graphics, robotics, and computer-assisted proofs. The purpose of this book is to be a concise but informative introduction to the theories of interval arithmetic as well as to some of their computational and scientific applications. Editorial Reviews "This new book by Hend Dawood is a fresh introduction to some of the basics of interval computation. It stops short of discussing the more complicated subdivision methods for converging to ranges of values, however it provides a bit of perspective about complex interval arithmetic, constraint intervals, and modal intervals, and it does go into the design of hardware operations for interval arithmetic, which is something still to be done by computer manufacturers." - Ramon E. Moore, (The Founder of Interval Computations) Professor Emeritus of Computer and Information Science, Department of Mathematics, The Ohio State University, Columbus, U.S.A. "A popular math-oriented introduction to interval computations and its applications. This short book contains an explanation of the need for interval computations, a brief history of interval computations, and main interval computation techniques. It also provides an impressive list of main practical applications of interval techniques." - Vladik Kreinovich, (International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems) Professor of Computer Science, University of Texas at El Paso, El Paso, Texas, U.S.A. "I am delighted to see one more Egyptian citizen re-entering the field of interval mathematics invented in this very country thousands years ago." - Marek W. Gutowski, Institute of Physics, Polish Academy of Sciences, Warszawa, Poland

Parametric Interval Algebraic Systems

Author : Iwona Skalna
Publisher : Springer
ISBN 13 : 3319751875
Total Pages : 211 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Parametric Interval Algebraic Systems by : Iwona Skalna

Download or read book Parametric Interval Algebraic Systems written by Iwona Skalna and published by Springer. This book was released on 2018-02-09 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book presents a framework for solving a general class of linear systems with coefficients being continuous functions of parameters varying within prescribed intervals. It also provides a comprehensive overview of the theory related to solving parametric interval linear systems and the basic properties of parametric interval matrices. In particular, it develops several new algorithms delivering sharp rigorous bounds for the solutions of such systems with full mathematical rigor. The framework employs the arithmetic of revised affine forms that enables the readers to handle dependent data. The book is intended not only for researchers interested in developing rigorous methods of numerical linear algebra, but also for engineers dealing with problems involving uncertain data. The theory discussed is also useful in various other fields of numerical analysis, in computer graphics, economics, computational geometry, computer-aided design, computer-assisted proofs, computer graphics, control theory, solving constraint satisfaction problems, and global optimization.

Interval Analysis

Author : Günter Mayer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110498057
Total Pages : 625 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 625 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

Interval Mathematics

Author : Karl Nickel
Publisher : Lecture Notes in Computer Science
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Interval Mathematics by : Karl Nickel

Download or read book Interval Mathematics written by Karl Nickel and published by Lecture Notes in Computer Science. This book was released on 1975-05-12 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Complexity and Feasibility of Data Processing and Interval Computations

Author : V. Kreinovich
Publisher : Springer Science & Business Media
ISBN 13 : 1475727933
Total Pages : 460 pages
Book Rating : 4.4/5 (757 download)

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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.

Complex Interval Arithmetic and Its Applications

Author : Miodrag Petković
Publisher : John Wiley & Sons
ISBN 13 : 9783527401345
Total Pages : 296 pages
Book Rating : 4.4/5 (13 download)

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Book Synopsis Complex Interval Arithmetic and Its Applications by : Miodrag Petković

Download or read book Complex Interval Arithmetic and Its Applications written by Miodrag Petković and published by John Wiley & Sons. This book was released on 1998 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present formulas and methods developed using complex interval arithmetic. While most of numerical methods described in the literature deal with real intervals and real vectors, there is no systematic study of methods in complex interval arithmetic. The book fills this gap. Several main subjects are considered: outer estimates for the range of complex functions, especially complex centered forms, the best approximations of elementary complex functions by disks, iterative methods for the inclusion by polynomial zeros including their implementation on parallel computers, the analysis of numerical stability of iterative methods by using complex interval arithmetic and numerical computation of curvilinear integrals with error bounds. Mainly new methods are presented developed over the last years, including a lot of very recent results by the authors some of which have not been published before.

Modal Interval Analysis

Author : Miguel A. Sainz
Publisher : Springer
ISBN 13 : 3319017217
Total Pages : 330 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 330 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.

Applications of Discrete Mathematics

Author : Richard D. Ringeisen
Publisher : SIAM
ISBN 13 : 9780898712193
Total Pages : 250 pages
Book Rating : 4.7/5 (121 download)

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Book Synopsis Applications of Discrete Mathematics by : Richard D. Ringeisen

Download or read book Applications of Discrete Mathematics written by Richard D. Ringeisen and published by SIAM. This book was released on 1988-01-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Mathematics and Parallel Computing

Author : Herbert Fischer
Publisher : Springer Science & Business Media
ISBN 13 : 3642997899
Total Pages : 371 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Applied Mathematics and Parallel Computing by : Herbert Fischer

Download or read book Applied Mathematics and Parallel Computing written by Herbert Fischer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors of this Festschrift prepared these papers to honour and express their friendship to Klaus Ritter on the occasion of his sixtieth birthday. Be cause of Ritter's many friends and his international reputation among math ematicians, finding contributors was easy. In fact, constraints on the size of the book required us to limit the number of papers. Klaus Ritter has done important work in a variety of areas, especially in var ious applications of linear and nonlinear optimization and also in connection with statistics and parallel computing. For the latter we have to mention Rit ter's development of transputer workstation hardware. The wide scope of his research is reflected by the breadth of the contributions in this Festschrift. After several years of scientific research in the U.S., Klaus Ritter was ap pointed as full professor at the University of Stuttgart. Since then, his name has become inextricably connected with the regularly scheduled conferences on optimization in Oberwolfach. In 1981 he became full professor of Applied Mathematics and Mathematical Statistics at the Technical University of Mu nich. In addition to his university teaching duties, he has made the activity of applying mathematical methods to problems of industry to be centrally important.

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.

Introduction to Interval Computation

Author : Gotz Alefeld
Publisher : Academic Press
ISBN 13 : 0080916368
Total Pages : 352 pages
Book Rating : 4.0/5 (89 download)

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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.

Invex-Infine functions and interval valued optimization

Author : Dr. Krishna Kummari
Publisher : Blue Rose Publishers
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4./5 ( download)

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Book Synopsis Invex-Infine functions and interval valued optimization by : Dr. Krishna Kummari

Download or read book Invex-Infine functions and interval valued optimization written by Dr. Krishna Kummari and published by Blue Rose Publishers. This book was released on 2022-09-27 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents optimality conditions and duality results for various types of nonsmooth programming problems with weaker assumptions. This book is an excellent resource for anyone interested in nonsmooth programming problem-solving approaches.

Scientific Computing, Validated Numerics, Interval Methods

Author : Walter Krämer
Publisher : Springer Science & Business Media
ISBN 13 : 1475764847
Total Pages : 385 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Scientific Computing, Validated Numerics, Interval Methods by : Walter Krämer

Download or read book Scientific Computing, Validated Numerics, Interval Methods written by Walter Krämer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scan 2000, the GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics and Interval 2000, the International Conference on Interval Methods in Science and Engineering were jointly held in Karlsruhe, September 19-22, 2000. The joint conference continued the series of 7 previous Scan-symposia under the joint sponsorship of GAMM and IMACS. These conferences have traditionally covered the numerical and algorithmic aspects of scientific computing, with a strong emphasis on validation and verification of computed results as well as on arithmetic, programming, and algorithmic tools for this purpose. The conference further continued the series of 4 former Interval conferences focusing on interval methods and their application in science and engineering. The objectives are to propagate current applications and research as well as to promote a greater understanding and increased awareness of the subject matters. The symposium was held in Karlsruhe the European cradle of interval arithmetic and self-validating numerics and attracted 193 researchers from 33 countries. 12 invited and 153 contributed talks were given. But not only the quantity was overwhelming we were deeply impressed by the emerging maturity of our discipline. There were many talks discussing a wide variety of serious applications stretching all parts of mathematical modelling. New efficient, publicly available or even commercial tools were proposed or presented, and also foundations of the theory of intervals and reliable computations were considerably strengthened.