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A Survey of Methods for the Estimation Ranges of Functions Using Interval Arithmetic

In: Models and Algorithms for Global Optimization

Author

Listed:
  • Julius Žilinskas

    (Institute of Mathematics and Informatics)

  • Ian David Lockhart Bogle

    (University College London)

Abstract

Interval arithmetic is a valuable tool in numerical analysis and modeling. Interval arithmetic operates with intervals defined by two real numbers and produces intervals containing all possible results of corresponding real operations with real numbers from each interval. An interval function can be constructed replacing the usual arithmetic operations by interval arithmetic operations in the algorithm calculating values of functions. An interval value of a function can be evaluated using the interval function with interval arguments and determines the lower and upper bounds for the function in the region defined by the vector of interval arguments.

Suggested Citation

  • Julius Žilinskas & Ian David Lockhart Bogle, 2007. "A Survey of Methods for the Estimation Ranges of Functions Using Interval Arithmetic," Springer Optimization and Its Applications, in: Aimo Törn & Julius Žilinskas (ed.), Models and Algorithms for Global Optimization, pages 97-108, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-36721-7_6
    DOI: 10.1007/978-0-387-36721-7_6
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    Cited by:

    1. Rahaman, Mostafijur & Mondal, Sankar Prasad & Alam, Shariful & Metwally, Ahmed Sayed M. & Salahshour, Soheil & Salimi, Mehdi & Ahmadian, Ali, 2022. "Manifestation of interval uncertainties for fractional differential equations under conformable derivative," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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