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| Author | : A. Neumaier |
| Publisher | : Cambridge University Press |
| Total Pages | : 275 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : 052133196X |
Mathematics of Computing -- Numerical Analysis.
| Author | : Bartłomiej Jacek Kubica |
| Publisher | : Springer |
| Total Pages | : 156 |
| Release | : 2019-03-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3030137953 |
This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals’ endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.
| Author | : Ramon E. Moore |
| Publisher | : SIAM |
| Total Pages | : 190 |
| Release | : 1979-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970906 |
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.
| Author | : Ramon E. Moore |
| Publisher | : SIAM |
| Total Pages | : 223 |
| Release | : 2009-01-01 |
| Genre | : Mathematics |
| ISBN | : 089871771X |
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 | : Eugene L. Allgower |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 788 |
| Release | : 1990-04-03 |
| Genre | : Mathematics |
| ISBN | : 9780821896945 |
Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.
| Author | : Ramon E. Moore |
| Publisher | : Elsevier |
| Total Pages | : 447 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483277844 |
Perspectives in Computing, Vol. 19: Reliability in Computing: The Role of Interval Methods in Scientific Computing presents a survey of the role of interval methods in reliable scientific computing, including vector arithmetic, language description, convergence, and algorithms. The selection takes a look at arithmetic for vector processors, FORTRAN-SC, and reliable expression evaluation in PASCAL-SC. Discussions focus on interval arithmetic, optimal scalar product, matrix and vector arithmetic, transformation of arithmetic expressions, development of FORTRAN-SC, and language description with examples. The text then examines floating-point standards, algorithms for verified inclusions, applications of differentiation arithmetic, and interval acceleration of convergence. The book ponders on solving systems of linear interval equations, interval least squares, existence of solutions and iterations for nonlinear equations, and interval methods for algebraic equations. Topics include interval methods for single equations, diagnosing collinearity, interval linear equations, effects of nonlinearity, and bounding the solutions. The publication is a valuable source of data for computer science experts and researchers interested in the role of interval methods in reliable scientific computing.
| Author | : Gotz Alefeld |
| Publisher | : Academic Press |
| Total Pages | : 352 |
| Release | : 2012-12-02 |
| Genre | : Mathematics |
| ISBN | : 0080916368 |
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 | : L. V. Kolev |
| Publisher | : World Scientific |
| Total Pages | : 328 |
| Release | : 1993 |
| Genre | : Technology & Engineering |
| ISBN | : 9789810214135 |
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.
| Author | : L Kolev |
| Publisher | : World Scientific |
| Total Pages | : 324 |
| Release | : 1993-09-23 |
| Genre | : Technology & Engineering |
| ISBN | : 9814504106 |
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.
| Author | : Eldon Hansen |
| Publisher | : CRC Press |
| Total Pages | : 528 |
| Release | : 2003-12-19 |
| Genre | : Mathematics |
| ISBN | : 9780203026922 |
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.
