Applications of Interval Computations:
a book

Keywords:

• Mathematical Modeling and Industrial Mathematics
• Numerical Analysis
• Control and Optimization
• Expert Systems

Applications of Interval Computations

Applied Optimization
Volume 3

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.

Contents and Contributors:

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. Hyvonen, 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.

Kluwer Academic Publishers, Dordrecht

Date of publishing: January 1996
444 pp.
Hardbound
ISBN: 0-7923-3847-2

Back to Books on Interval Computations

Back to Applications of Interval Computations

Back to the main menu of the Interval Computations website