Synopses & Reviews
Applications of Interval Computations contains primarily survey articles of actual industrial applications of numerical analysis with automatic result verification and of interval representation of data. Underlying topics include branch and bound algorithms for global optimization, constraint propagation, solution sets of linear systems, hardware and software systems for interval computations, and fuzzy logic. Actual applications described in the book include economic input-output models, quality control in manufacturing design, a computer-assisted proof in quantum mechanics, medical expert systems, and others. A realistic view of interval computations is taken: the articles indicate when and how overestimation and other challenges can be overcome. An introductory chapter explains the content of the papers in terminology accessible to mathematically literate graduate students. The style of the individual, refereed contributions has been made uniform and understandable, and there is an extensive book-wide index.
Audience: Valuable to students and researchers interested in automatic result verification.
Synopsis
Applications of Interval Computations contains primarily survey articles of actual industrial applications of numerical analysis with automatic result verification and of interval representation of data. Underlying topics include branch and bound algorithms for global optimization, constraint propagation, solution sets of linear systems, hardware and software systems for interval computations, and fuzzy logic. Actual applications described in the book include economic input-output models, quality control in manufacturing design, a computer-assisted proof in quantum mechanics, medical expert systems, and others. A realistic view of interval computations is taken: the articles indicate when and how overestimation and other challenges can be overcome. An introductory chapter explains the content of the papers in terminology accessible to mathematically literate graduate students. The style of the individual, refereed contributions has been made uniform and understandable, and there is an extensive book-wide index. Audience: Valuable to students and researchers interested in automatic result verification.
Synopsis
Primary Audience for the Book - Specialists in numerical computations who are interested in algorithms with automatic result verification. - Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc- cessful applications. - Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e., appli- cations of numerical methods with automatic result verification, that were pre- sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, 0. 9,1. 1] + 2. 9,3. 1] = 3. 8,4. 2], where 3. 8,4. 2] = {x + ylx E 0. 9,1. 1] and y E 3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.
Table of Contents
Preface.
1. Applications of Interval Computations: An Introduction;
R.B. Kearfott, V. Kreinovich. 2. A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems;
R.B. Kearfott. 3. The Shape of the Symmetric Solution Set;
G. Alefeld, et al. 4. Linear Interval Equations: Computing Enclosures with Bounded Relative Overestimation is NP-Hard;
J. Rohn. 5. Quality Improvement Via Optimization of Tolerance Intervals During the Design Stage;
S. Hadjihassan, et al. 6. Applications of Interval Computations to Regional Economic Input-Output Models;
M.E. Jerrell. 7. Interval Arithmetic in Quantum Mechanics;
C.L. Fefferman, L.A. Seco. 8. Interval Computations on the Spreadsheet;
E. Hyvönen, S. De Pascale. 9. Solving Optimization Problems with Help of the UniCalc Solver;
A.L. Semenov. 10. Automatically Verified Arithmetic on Probability Distributions and Intervals;
D. Berleant. 11. Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications;
H.T. Nguyen, V. Kreinovich. 12. Fuzzy Interval Inference Utilizing the Checklist Paradigm and BK-Relational Products;
L.J. Kohout, W. Bandler. 13. Computing Uncertainty in Interval Based Sets;
L.M. Rocha, et al. 14. Software and Hardware Techniques for Accurate, Self-Validating Arithmetic;
M.J. Schulte, E.E. Swartzlander, Jr. 15. Stimulating Hardware and Software Support for Interval Arithmetic;
G.W. Walster. Index.