Applications of Interval Computations: An Introduction

  • R. Baker Kearfott
  • Vladik Kreinovich
Part of the Applied Optimization book series (APOP, volume 3)


The main goal of this introduction is to make the book more accessible to readers who are not familiar with interval computations: to beginning graduate students, to researchers from related fields, etc. With this goal in mind, this introduction describes the basic ideas behind interval computations and behind the applications of interval computations that are surveyed in the book.


Constraint Propagation Interval Arithmetic Global Optimization Problem Interval Computation Roundoff Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Alefeld, V. Kreinovich, and G. Mayer, “The Shape of the Symmetric Solution Set,” This Volume.Google Scholar
  2. [2]
    D. Berleant, “Automatically Verified Arithmetic on Probability Distributions and Intervals”, This Volume.Google Scholar
  3. [3]
    C. L. Fefferman and L. A. Seco, “Interval Arithmetic in Quantum Mechanics”, This Volume.Google Scholar
  4. [4]
    R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman Lectures On Physics, Addison-Wesley, Redwood City, CA, 1989.Google Scholar
  5. [5]
    S. Hadjihassan, E. Walter, and L. Pronzato, “Quality Improvement via The Optimization Of Tolerance Intervals During The Design Stage,” This Volume.Google Scholar
  6. [6]
    R. Hammer, M. Hocks, U. Kulisch, D. Ratz, Numerical toolbox for verified computing. I. Basic numerical problems, Springer Verlag, Heidelberg, N.Y., 1993.Google Scholar
  7. [7]
    E. R. Hansen, Global optimization using interval analysis, Marcel Dekker, N.Y., 1992.zbMATHGoogle Scholar
  8. [8]
    E. Hyvönen and S. De Pascale, “Interval Computations on the Spreadsheet”, This Volume.Google Scholar
  9. [9]
    M. E. Jerrell, “Applications of Interval Computations to Regional Economic Input-Output Models,” This Volume.Google Scholar
  10. [10]
    R. B. Kearfott, “A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems,” This Volume.Google Scholar
  11. [11]
    L. J. Kohout and W. Bandler, “Fuzzy Interval Inference Utilizing the Checklist Paradigm and BK-Relational Products”, This Volume.Google Scholar
  12. [12]
    V. Kreinovich (ed.), Reliable Computing, 1995, Supplement (Extended Abstracts of APIC’95: International Workshop on Applications of Interval Computations, El Paso, TX, Febr. 23-25, 1995).zbMATHGoogle Scholar
  13. [13]
    R. E. Moore, Automatic error analysis in digital computation, Lockheed Missiles and Space Co. Technical Report LMSD-48421, Palo Alto, CA, 1959.Google Scholar
  14. [14]
    R. E. Moore and C. T. Yang, Interval analysis, Lockheed Missiles and Space Co. Technical Report LMSD-285875, Palo Alto, CA, 1959.Google Scholar
  15. [15]
    R. E. Moore, Interval analysis, Prentice Hall, Englewood Cliffs, NJ, 1966.zbMATHGoogle Scholar
  16. [16]
    H. T. Nguyen and V. Kreinovich, “Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications”, This Volume.Google Scholar
  17. [17]
    P. M. Pardalos and J. B. Rosen, Constrained Global Optimization: Algorithms and Applications, Springer-Verlag, New York, 1987.zbMATHCrossRefGoogle Scholar
  18. [18]
    L. M. Rocha, V. Kreinovich, and R. B. Kearfott, “Computing Uncertainty in Interval Based Sets”, This Volume.Google Scholar
  19. [19]
    J. Rohn, “Linear Interval Equations: Computing Enclosures with Bounded Relative Or Absolute Overestimation is NP-Hard,” This Volume.Google Scholar
  20. [20]
    M. J. Schulte and E. E. Swartzlander, Jr., “Software and Hardware Techniques for Accurate, Self-Validating Arithmetic,” This Volume.Google Scholar
  21. [21]
    A. L. Semenov, “Solving Optimization Problems with Help of the UniCalc Solver,” This Volume.Google Scholar
  22. [22]
    G. W. Walster, “Stimulating Hardware and Software Support for Interval Arithmetic,” This Volume.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • R. Baker Kearfott
    • 1
  • Vladik Kreinovich
    • 2
  1. 1.Department of MathematicsUniversity of Southwestern LouisianaLafayetteUSA
  2. 2.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

Personalised recommendations