Interval Mathematics
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Methods And Applications Of Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher: SIAM
Release Date : 1979-01-01
Methods And Applications Of Interval Analysis written by Ramon E. Moore and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-01-01 with Mathematics categories.
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 Mathematics
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Author : Karl Nickel
language : de
Publisher: Lecture Notes in Computer Science
Release Date : 1975-05-12
Interval Mathematics written by Karl Nickel and has been published by Lecture Notes in Computer Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-05-12 with Computers categories.
Theories Of Interval Arithmetic
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Author : Hend Dawood
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-10-07
Theories Of Interval Arithmetic written by Hend Dawood and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-07 with Mathematics categories.
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
Interval Mathematics 1980
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Author : Karl L. E. Nickel
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Interval Mathematics 1980 written by Karl L. E. Nickel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
Interval Mathematics
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Author : K. Nickel
language : en
Publisher:
Release Date : 2014-01-15
Interval Mathematics written by K. Nickel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Interval Mathematics
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Author :
language : de
Publisher:
Release Date : 1975
Interval Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Interval Mathematics 1985
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Author : Karl Nickel
language : en
Publisher: Springer
Release Date : 1986
Interval Mathematics 1985 written by Karl Nickel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Modal Interval Analysis
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Author : Miguel A. Sainz
language : en
Publisher: Springer
Release Date : 2013-11-18
Modal Interval Analysis written by Miguel A. Sainz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-18 with Mathematics categories.
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.
Introduction To Interval Computation
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Author : Gotz Alefeld
language : en
Publisher: Academic Press
Release Date : 2012-12-02
Introduction To Interval Computation written by Gotz Alefeld and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
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.
Interval Analysis
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Author : Günter Mayer
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-10
Interval Analysis written by Günter Mayer and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-10 with Mathematics categories.
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