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

  • Julius Žilinskas
  • Ian David Lockhart Bogle
Part of the Optimization and Its Applications book series (SOIA, volume 4)


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.


Global Optimization Interval Function Interval Arithmetic Sample Standard Deviation Estimation Range 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Julius Žilinskas
    • 1
  • Ian David Lockhart Bogle
    • 2
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania
  2. 2.Centre for Process Systems Engineering, Department of Chemical EngineeringUniversity College LondonLondonUK

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