Theories of Interval Arithmetic: Mathematical Foundations and Applications

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 Book Description 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. About the Author: Hend Dawood is presently working in the Department of Mathematics at Cairo University, with more than eight years of research experience in the field of computational mathematics. Her current research interests include algebraic systems of interval mathematics, logical foundations of computation, proof theory and axiomatics, ordered algebraic structures and algebraic logic, uncertainty quantification, and uncertain computing. She authored a monograph on the foundations of interval mathematics and a number of related publications. Hend Dawood is an Associate Editor for the International Journal of Fuzzy Computation and Modeling (IJFCM – Inderscience); and serves as a Reviewer for a number of international journals of repute in the field of computational mathematics including Neural Computing and Applications (NCA – Springer Verlag), the Journal of the Egyptian Mathematical Society (JOEMS – Elsevier), Alexandria Engineering Journal (AEJ – Elsevier), and Coupled Systems Mechanics (CSM – Techno-Press). She is a member of the Egyptian Mathematical Society (EMS), a member of the Cairo University Interval Arithmetic Research Group (CUIA), and a voting member of the IEEE Interval Standard Working Group (IEEE P1788). As recognition of her professional contribution and activities, Hend Dawood is recipient of many research and academic awards.