Applications of Interval Computations

1. Front Matter

   Pages i-xvii

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2. Applications of Interval Computations: An Introduction

   • R. Baker Kearfott, Vladik Kreinovich

   Pages 1-22

3. A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems

   • R. Baker Kearfott

   Pages 23-59

4. The Shape of the Symmetric Solution Set

   • Götz Alefeld, Vladik Kreinovich, Günter Mayer

   Pages 61-79

5. Linear Interval Equations: Computing Enclosures with Bounded Relative Overestimation is NP-Hard

   • Jiří Rohn

   Pages 81-89

6. Quality Improvement via Optimization of Tolerance Intervals During the Design Stage

   • Sevgui Hadjihassan, Eric Walter, Luc Pronzato

   Pages 91-131

7. Applications of Interval Computations to Regional Economic Input-Output Models

   • Max E. Jerrell

   Pages 133-143

8. Interval Arithmetic in Quantum Mechanics

   • Charles L. Fefferman, Luis A. Seco

   Pages 145-167

9. Interval Computations on the Spreadsheet

   • Eero Hyvönen, Stefano De Pascale

   Pages 169-209

10. Solving Optimization Problems with Help of the UniCalc Solver

    • Alexander L. Semenov

    Pages 211-225

11. Automatically Verified Arithmetic on Probability Distributions and Intervals

    • Daniel Berleant

    Pages 227-244

12. Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications

    • Hung T. Nguyen, Vladik Kreinovich

    Pages 245-290

13. Fuzzy Interval Inference Utilizing the Checklist Paradigm and BK-Relational Products

    • L. J. Kohout, W. Bandler

    Pages 291-335

14. Computing Uncertainty in Interval Based Sets

    • Luis Mateus Rocha, Vladik Kreinovich, R. Baker Kearfott

    Pages 337-380

15. Software and Hardware Techniques for Accurate, Self-Validating Arithmetic

    • Michael J. Schulte, Earl E. Swartzlander Jr.

    Pages 381-404

16. Stimulating Hardware and Software Support for Interval Arithmetic

    • G. William Walster

    Pages 405-416

17. Back Matter

    Pages 417-427

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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.

• algorithms
• applied mathematics
• fuzzy
• fuzzy set
• fuzzy sets
• global optimization
• mathematics
• mechanics
• numerical method
• optimization
• probability
• probability distribution
• quantum mechanics
• uncertainty
• verification

• University of Southwestern Louisiana, USA

  R. Baker Kearfott

• University of Texas at El Paso, USA

  Vladik Kreinovich

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