Download or read book A Theoretical Application of the Concept of Interval Arithmetic to Certain Selected Topics of Numerical Analysis written by John Henry Knox and published by . This book was released on 1969 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
Download or read book Topics in Interval Analysis written by Eldon R. Hansen and published by . This book was released on 1969 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Classical and Modern Numerical Analysis written by Azmy S. Ackleh and published by CRC Press. This book was released on 2009-07-20 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.The text covers the main areas o
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.
Download or read book Interval Methods For Circuit Analysis written by L Kolev and published by World Scientific. This book was released on 1993-09-23 with total page 324 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.
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.
Download or read book Applications of Number Theory to Numerical Analysis written by S. K. Zaremba and published by Academic Press. This book was released on 2014-05-10 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.
Download or read book Theory and Applications of Numerical Analysis written by G. M. Phillips and published by Elsevier. This book was released on 1996-07-05 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. a unique blend of theory and applications two brand new chapters on eigenvalues and splines inclusion of formal algorithms numerous fully worked examples a large number of problems, many with solutions
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.
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.
Download or read book Introduction to Numerical Analysis written by J. Stoer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d ing up the convergence of discretization methods in connection with Romberg integration are explained at length.
Download or read book Numerical Methods in Scientific Computing written by Germund Dahlquist and published by SIAM. This book was released on 2008-01-01 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book from the authors of the classic book Numerical methods addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines traditional and well-developed topics with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLAB multiple precision package; and a guide to literature, algorithms, and software in numerical analysis. Review questions, problems, and computer exercises are also included. For use in an introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.
Download or read book Applications of Interval Computations written by R. Baker Kearfott and published by Boom Koninklijke Uitgevers. This book was released on 1996-01-31 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a February 1994 international workshop held in El Paso, Texas, survey industrial applications of numerical analysis with automatic result verification, and of interval representation of data. After an introductory chapter explaining the content of the papers in terminology accessible to mathematically literate graduate students, chapters describe applications such as economic input-output models; quality control in manufacturing design; and medical expert systems, focusing on dealing with problems such as overestimation. Other topics include branch and bound algorithms for global optimization; fuzzy logic; and constraint propagation. For students and researchers interested in automatic result verification. Annotation copyright by Book News, Inc., Portland, OR
Download or read book KWIC Index for Numerical Algebra written by Alston Scott Householder and published by . This book was released on 1972 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
